1. As long as you have no individual contract with the bank that states otherwise,you are sadly out of luck. While banks must keep their service accessible, they can absolutely regulate how to access them as long it falls within reasoning.

2. There is a high likelihood that you can also use pure Chromium so you can at least stay off Google.

3. There has been a case in Germany when a bank changed it’s TAN process and customers didn’t want to change over to photoTAN/SMSTAN. It went through the court system and the highest federal court referred the case to the EU courts who afaik didn’t even accept it and did not see any problems. So it’s unlikely that there are any EU rules against it.

4. I think that there was a similar discussion around edge/IE and the result was the same.

Personally I would try a user agent switcher,if that doesn’t work chromium,if that does not work Chrome portable. The bank already knows everything and portable with a good firewall keeps google at bay.