We need Linux on phones. Bank apps not needed as long as I can use browser. But do need some things like wireless cards, popular apps like Sonos and Spotify working.
Unfortunately many banks in the UK no longer offer a web portal or physical branches.
I'd love to see legislation that mandated a functioning web experience for critical services like this (banking, utilities, etc) - otherwise it will continue to further entrench the current duopoly.
(I suppose this is also an instance where I should do a better job of voting with my feet and supporting services that do offer this)
Need to pressure banks to achieve feature parity between their websites and native apps. I'm forced to use Paypal to remote deposit checks because my banks limit that feature to their apps, which I can't use because of my device's age. (Paypal does, too, but their app still works for now.)
We need unlockable bootloaders on ALL phones. Then many more OSes will come
Unfortunately these days bank apps are required by the banks for "security", and good luck getting anything done without the bank app installed on your phone.
The only other alternative available is SMS but that is being phased out (rightly so) for being insecure.
GrapheneOS is what you're looking for
Lots of questionable replies to you here, people recommending Android/Lineage/Graphene are being silly, Sailfish is a better answer but with major proprietary components I would still skip it. postmarketOS is the best option I believe. Mobian and some others possibly worth a mention as well. I found Ubuntu Touch/ubports to be disappointing so I wouldn't bother with that either. You can check the pmOS wiki to find compatible devices. Perhaps check first if anything you already own has support, and help them support your device better if you are able. Otherwise look for the devices with the best support and get one off eBay. Librem 5 and PinePhone should be among the best supported devices but you may get better performance / $ with a OnePlus 6T or other formerly-Android phone (again, verify most stuff is already working before buying something if possible).
For the popular apps you mention, there is Waydroid to run Android apps.