Quantum So I've been fiddling around for several minutes at this point and here's what I've discovered although I don't really get the "why" behind it.
I got myself Firefox to see how that works with my bank website and although the keyboard doesn't show Bitwarden instantly, if I press the card field and then the password field, in the password field makes the Bitwarden prompt show up, just not the card field for some reason. So I guess since it really doesn't matter to me, I could use Firefox for my banking.
I cannot reproduce the above with Brave with the things I've tried. Unblocking fingerprinting doesn't help, allowing more ads to be displayed doesn't help (I have shields on aggressive always unless something breaks), and lastly I tried to allow more cookies to be used (third party cookies). So far nothing has worked to make Bitwarden pop up in the keyboard while using Brave.
Any way, like I said, Firefox appears to be working with my bank, but thanks for your time and effort. :) I wish I knew/understood why Brave won't work with my bank.