How do you daily drive an Android 4 device in 2023?

You don't. Old versions of Android are incredibly insecure and are often targeted by botnets and compromised websites/ad networks. Not only would you be putting your accounts at risk, you could be at risk of getting into trouble with the law, if the hackers/bots decide to use your device as part of a DDoS attack, or as a proxy server for conducting illegal activities. Of course, it may eventually come to light that you're innocent, but good luck dealing with the cops, bureaucracy, bad reputation and stress that comes with such an event.

TL;DR: Not worth it, unless you like inviting trouble. Best to send it off to an e-waste recycling center.

You could put lineage OS on it, and that might make it a little bit more secure, but I wouldn't trust it still. Might be good for internal network stuff like making it a webcam, remote control for your TV and stuff.

I carry a Droid 4 (because I like the keyboard) which was running Android 4. Which was absolutely unusable for the web, but alright for ssh, xmpp, and as a camera.

A few weeks ago I replaced android on it with Linux (Maemo Leste) which is... great but also very rough.

I mostly use my phone as a wifi remote to control my computer. That's working much better now than under android.

But the camera doesn't work. Ugh.

Thanks for all the advice and feedback! Granted that it's not that secure running an extremely old android system, but in reality the devices will only be turned on for no more than 4 hours a month, I don't think it's a big concern. I think I'd use via for browsing and newpipe for YouTube as they seemed to still support old systems and are relatively light-weight. I'd let you guys know how it went down if possible.

Absolutely!

Google still supports Google Play Services with security updates, and many of their apps and services are still updated via on-the-fly updates (non-app updates).

You can use the latest Youtube app compatible, it will most likely work. If not, just use the browser for it. Version 16.40.36 from October 16, 2021 is the latest one compatible with Android 5

Firefox still supports Android 5, and is the minimum requirement.

You can use AirDroid to mirror the screen of your phone to a desktop computer. Minimum requirement for it is Android 4.4

I used a Android 2.3.7 device for 2 weeks 6 months ago that goes to the internet using Via Browser, had GPS using a 2014 version of Maps still working to this day, old videogames still installed and called and sent SMSs just fine. You'll be fine.