You keep saying “across the entire economy” but not every sector of the economy was equally affected.

Sure, but the proponents of "greedflation" are generally describing across-the-board simultaneous price increases across a ton of different industries. To be sure, inflation always has different latency periods for different industries.

Also, there is good competition in some sectors (where it’s easy and cheap to produce the product and the supply chain isn’t very complicated) and definitely not others. Look at gas prices, which were involved in a lot of the inflation and its secondary effects. You can save a few cents here or there by shopping around, but otherwise the price is relatively similar (and relatively high) everywhere you look in an area.

So, I mean, your basic premise is true that competition affects price behavior. I would caution against going for the interpretation that just because something is expensive or complicated to produce, that's going to result in a lack of competition. Oil/gas specifically is a global industry. The market breaks down into coordinated nationally-owned orgs (OPEC, mostly Middle Eastern/African) and publicly traded oil producers (Shell, Exxon etc). Now, to be sure, we all know the industry is shady as fuck, influences global wars, etc. But regardless, these interests are still in competition with each other on the open market. Shell and Exxon don't have monopoly licenses to import oil to the U.S., the commodity is traded openly. At the local level, this breaks down into gas stations (either franchise/branded or independent, which reflects in the term of the contract the station has with their provider). These days, we do have trivial ability to comparison shop between providers (Google Maps even has the price when you search for gas stations). So there is market pricing feedback at all levels. A company that tries to price gouge can be undercut. The reason you see similar prices isn't really evidence either way - that's exactly what you'd expect to see in a competitive industry where the quality of the product isn't that variable. It's certainly not impossible that ten, twenty big oil corps could conspire to coordinate prices, but that specific thing remains to be proven. As for why they achieved such high profits in the last few years, esp. in 2022, well, the simple explanation would be that they didn't pay as much to produce their existing stock and the global instability in the market created a bidding war for the available supplies, especially for oil as Russia's gas supply to Europe was cut. You can call that "price gouging" but that's how markets operate, the whole point is that transitory increases in prices are supposed to incentivized increased production to alleviate a supply crunch, and vice versa when prices sink.

The topic in general does raise deeper questions like, why do private companies get to profit heavily off of preexisting natural resources, but that's another topic.

Now re: telecoms - this is a whole second issue. There are single providers in a lot of areas, for a bunch of reasons (PITA to deploy to rural places, municipal agreements limiting telecom deployment to a single provider, etc.). That is more "infrastructure" like, ergo, what most people would say is more deserving of being run by government, or IMO, by NGO non-profits/cooperatives. I know firsthand the BS Comcast pulls with jacking up their prices to $200/mo or whatever when they can get away with it.

A huge part of inflation is still rising rental rates. In my city about six companies own most of the large apartment buildings that people live in. Something tells me they’d have no problems raising rents between the six of them just because they easily can.

That's the far end of the spectrum tbh, competition in property/rentals is very high and generally non-monopolized. You may see six major companies controlling a lot of rentals locally (exact numbers would be useful here), but you also have individuals being able to rent their own property, you have the fact that people do have the option to go elsewhere - for the question of price fixing, the threshold is basically just, is there enough competition that one provider can't just arbitrarily decide to increase their prices without losing market share. If you raise prices and people move to another provider, well, you can't really price gouge. It's not unheard of to have a price-fixing cartel, but it's not just something you can assume exists by default.