There is this [LIST] Banking Apps that work on /e/OS.
I would not go along with a bank that wanted me to jump though hoops to use their services. I would write to them to tell them that they must organise the security of a connection with you – that you do not want Google involved.
Sorry, I do not follow “banking app on my PC” … on your PC your banking is via a browser and https? That is what I use (when notes and coins run out).