Regarding banking apps and things like that, I don't run into to any issues except for not being able to scan checks for deposit on the mobile website. And also I have to have physical credit cards. If you can't do what you need, consider changing to a local credit union which has your interests in mind far more than a for-profit bank.
I've never run into a need for apps for a government purpose, but perhaps I will someday.
I'm sure my situation where I live may be different than your situation where you live.
I don't use an open source fork of Android daily and from what I can tell the best option that exists today.
The only hardware that I know will continue to be open enough for this to be viable in the future is Fairphone. I hope there are others. I would definitely would NOT trust Google Pixel to remain open for the foreseeable future.
Personally, I'm trying to get out of the habit of using my phone anyway, so I might as well have laptop or desktop hardware that can fulfill my needs.
I have no requirement to use apps other than calls, navigation, something to let me view pdf, take photos and maybe browse HN :) (already a big bunch)
Anyway, for navigation, try out Organic Maps. It's not as good as Google Maps in some ways, but in other ways it's better. I'm honestly very impressed with it as an open source project. I think you have to use a Google signed version of it to run it on Android Auto though, but honestly, maybe it's better just to have a phone holder instead of the finicky Android Auto experience that at least I go through.
Also observing new apps showing up on my phone after Android update without me ever installing them made me so angry that I stopped updating my phone, you know- apps that cannot be removed or disabled.. it constantly makes me wonder what really is running in the background- I don't even have a way to reliably list those things. I'm going to sit through the list you provided and push myself to go through the last mile to actually make the move.
Problem will be with banking apps and such, well you can get an used iphone and in lockdown mode it should be fine even if it reaches EoL.