I have a profile with Google Play installed purely for banking apps only (No Google Play anywhere else). NatWest, Starling, Revolut, you name it, works. (I have no Barclay's though!). If Barclay's is a still persistent problem I'd try to install Google Play on the owner's profile, disable it and push it to the other profile and install Barclay's there (I never tried it but it could help).
Brave browser password auto fill works great. What doesn't work great if you're using Obtainium (Brave without Google Play) is the Sync feature allowing you importing all stuff from you desktop, etc.
There's also great FOSS app called KeePassXC - Cross platform password manager. It also supposed to auto fill passwords from the database stored in your phone, and with proper app's privilege to access the keyboard I think (I am still about to explore this option and I'd like to know others opinion).