FWIW, the shield backpack and either AMR or Quasar/EAT have served me well against bots, but I typically run light armor. I bring the grenade pistol to handle factories.

If you aren't already using it, there's never been a better time to get into the AMR now that they buffed the damage and finally zeroed in the scope.

If everyone you're with is taking every engagement you don't have to be with them. Just do the mission. Kills don't count

Armor is medium with crouch bonus.

If you're willing to spend SC on armor, try to get the FS-38 Eradicator armor from the rotating shop. To my knowledge it's the only light armor with the Fortified mod ("Further reduces recoil when crouching or prone by 30%. Provides 50% resistance to explosive damage."). I think that's the armor mod you're already running, just in light armor. I don't find 50 armor makes much difference, but the extra mobility really does. The recoil bonus is whatever, with that armor mod vs. bots the explosive resist is the real juice.

For clarity, the Fortified bonus to explosive resist doesn't require you to crouch or go prone to get its effect, you only need to crouch to get the recoil bonus. With Fortified you can sprint around and get hit by a rocket, or run over a bot mine, and not die if you've got full health. There's a separate bonus vs. explosive damage from crouching or going prone, but that's universal and not tied to any armor mod.

everyone is getting there faster and killing things faster because they got there earlier

Could be because they were wearing light armor. Armor seems to provide a really poor rate of return in this game, but light armor's bonuses to speed and stamina regen pay sizable dividends.

Adjudicator

My go-to primary vs. bots used to be the pre-nerf Slugger (RIP sweet prince), now it's the JAR-5 Dominator. In both cases it was because the weapon could handle Devastators. If I run out of AC ammo while facing down Heavy and/or Rocket Devastators, being able to switch to a primary that can stagger and kill one can save me. JAR-5 does take some getting used to though. It's 3rd-person handling is poor, but it's tolerable in 1st-person so that's generally what I use with that gun. The JAR-5 also has relatively slow bullet travel time that you have to account for. Now that I'm used to it though, I don't find any other primary as effective vs. bots.

mortar sentry

I've never found the mortar sentry all that effective vs. bots, they don't seem to clump up as much as bugs do. EMS Mortar can be a pretty good option for crowd control though. Personally I run laser (for major objectives or Eye of Sauron towers), Eagle Strike (for small bases and patrols) and Eagle 500 (mostly for tanks, walking factories; AC can take out tanks but oftem it's just quicker to 500 it).

I try to branch out but almost always drift back to something like:

Regular Breaker

Autocannon

Walking barrage

Eagle airstrike

EMF turret

Bots are easy until you get into level 8 games with the Solo Sprint Brothers that aggro the whole map.

Personal opinion: adjudicator just doesn't have a enough ammo per mag to deal with bots quickly. If you have access to it, the Dominator will deal with bots much quicker due to its explosive damage. You can shoot the front miniguns off a factory strider with it, and it takes less than 2 mags to kill one if you run up and shoot it in the belly. Only caveat with the Dominator is that is has a lot of sway and the rounds are rocket propelled, meaning they're moving slowest when they exit the barrel, and accelerate at the target. I have found that I have to aim in 1st person to actually hit mid and long shots.

If the Dominator isn't available to you, the Scorcher it super fast at getting on target and putting rounds on target. The explosive damage punches through a lot of armor for quick kills (3 shots on a chicken walker's crotch.

I love the auto cannon, but there are some situations when you want either an EAT or the Orbital Rail to deal with tanks and turrets quickly. If you have access to it, the stun grenade pairs really well with Auto cannon, especially for stopping hulks.

I used to exclusively run the Quasar, but with the recent nerf, I find it way too slow to be effective.

I would also recommend trying different things, the Diligence CS is now an absolute beast at one shotting bots with headshots, and the Slugger can too, but both require accurate headshots from first person.

One thing to note, all my opinions are based on usually playing difficulty 9, sometimes 7 and 8.

Headshots are OP against bots.

I tend to prefer the liberator, I set it to burst or even single fire, calmly ADS, and then one shot all normal bots, one by one.

You can take down the piloted walkers in one shot, too, if you can hit the guy riding it.

Bigger bots I tend to spam bullets at a bit more, but for them too, headshots are extremely effective.

On the contrary of "go slower," I suggest you actually move faster. Bots cause issues when dropships come in. Sometimes, even when you're doing everything right, you can still get a flare set off, and if you're trying to clear a base and a dropship comes in, it gets a hell of a lot harder. The longer the mission goes on, the stronger the bot patrols and reinforcements get, so the best option is to treat almost everything like a blitz mission.

Most of what I'm gonna say, you probably already know given your loadout. The big difference between bot outposts and bug nests is that you don't need an angle for a guaranteed airstrike to take out a factory. If you're running the autocannon, you can take out factories if you're in front of them from a hell of a distance. Just aim for the upper part of the vent from within about 45 degrees of dead-on, and the factory goes up. If a flare goes off, it'll be dropped on the bot calling it in, and by the time they land, they won't have any idea where you are if you run. If you can't get line-of-sight on a vent, run up, call in an Eagle Airstrike, and run off again. For light and medium outposts, you can get in and out in no time.

For just regular patrols though, if you have to engage, engage at a distance. I'd swap out the mortar sentry for an autocannon sentry, mostly because it brings more immediate results, with less of a chance of killing you if the bots get too close. If you shoot at them from a distance, they're more likely to have less time to react, and not get a flare off, which again, is the worst outcome of engaging. Deal with it, and move on. Don't get bogged down in engagement.

Aside from that, the only real change I'd make is swapping out the orbital laser for the orbital rail cannon. You're not limited to just 3 uses, and while your autocannon can deal with sneak attacks on big bots, sometimes you just need to delete something. If they're close enough together, I've even seen it take out 2 hulks. You can get rid of a big threat every two and a half minutes, and not sacrifice speed. Only other difference between your loadout and mine is that I'm using the Liberator as my primary, but if you're happy with the Adjudicator, keep it.

For your team wanting to shoot everything, if they're going to insist on drawing aggro, let them. Do objectives, be proactive. You get a lot more bots from an area filled with outposts than an area empty of them, and you'll lessen the number they have to fight. Finish a spot, move onto the next, and do it fast.

One minor thing, factory striders. These things were built to withstand tons of air strikes, and even eat orbital lasers and rail cannons. But if you take off the machine guns on its chin, and walk up to it and unload on its belly with the autocannon, they go down very fast. The biggest challenge will be getting your team to stop calling in airstrikes so you can do it.

Since it seems like your teammates are often Leroy Jenkins-ing their way into every engagement, it might be a good idea to consider switching to more of a support role. I've found that the Diligence Counter-Sniper works really well against bots after the recent buff (it will one-shot every Devastator type if you can land a headshot, and one-shots every infantry unit to the body), and it keeps you pretty safe from afar. Replacing the mortar sentry with the EMS mortar will also do you some favors, as it'll be less likely to kill your teammates, and also keeps enemy movement suppressed, keeping you safer for longer, and makes landing those headshots on Devastators a lot easier.

Since you seem to mostly play on Difficulty 4, I'd recommend dropping the Autocannon for something else. AC is hella fun, but it's also hella overkill for lower difficulties, as you won't be dealing with Factory Striders, Gunships, or Hulks at level 4 (I think Hulks will spawn at 4, but they're scarce). I'd recommend swapping the AC for a shield generator backpack instead, as this will make better use of your available strategem slots for this difficulty. If you're using the AC for bot fabricators, those can be easily dealt with by using Eagle airstrikes or the grenade pistol.

I'd also consider replacing the orbital laser, as well. You only get 3 per mission, and there's a pretty good cooldown between uses, so chances are you likely end up saving them for "when you really need it", and end up finishing the mission without using it hardly at all. I'd switch this one out for a different support weapon; I suggest the laser cannon, but any non-backpack support weapon will be a good use of this strategem slot, IMO. Alternatively, you could also go without any support weapon at all, and pick one up off the ground or a dead teammate. At Difficulty 4, you can do a surprising amount with just your primary and strategems, so you could also consider swapping this for something like orbital gas or even just a precision strike.

I feel like these mixups to your loadout will offer you a lot more flexibility to your missions, while allowing you to secure objectives safely and keeping your teammates safe.

I was enjoying plasma primary, grenade pistol and AM rifle the other day.

Killing hulks with slit-shots feels great and grenade pistol can hit factories from quite far.

Depending on other team loadouts I'll take airstrike or mortar or 500kg and shield backpack.

Are you playing on level 9?

If you enjoy assault rifles I strongly recommend the sickle. It's one of the most accurate weapons in the game and effectively has infinite ammo. If your aim is decent you can drop most enemies before it overheats. You're not going to be topping the kill count, but that isn't the point of the game.

Someone else mentioned the Quasar/EAT and I cannot echo that loudly enough. I prefer the Quasar for bots due to the increased frequency that I find myself needing anti-tank but it's a little more difficult to use than the EAT.

Everyone wants to stick to the Autocannon meta but it really doesn't work for me and there are some jobs that other tools do better. I can take out dropships with the EAT all day long where as the Autocannon can only hope to knock the bots off the bottom at best. This also frees up you backpack for the shield generator, which IS a crutch but will allow you a ton of breathing room against the bots in particular.

For armor against the bots you really want the perk that reduces explosive damage. The bots' laser fire isn't all that bad but for whatever reason they have pinpoint accuracy with rockets.

I don't think that avoiding bot patrols is the right answer. You really want to avoid ACCIDENTALLY engaging bot patrols or engaging them before the team is prepared. If you can get the drop on a patrol it's almost trivial for a team of helldivers to wipe them out without triggering dropships.

This game really thrives on communication, so encouraging any kind of dialogue between your team members is the best way to improve how your missions go.