lbschenkel Thank you for sharing this. I can confirm that the app no longer complains about an accessibility service when TalkBack is disabled in the profile where the Nordea app is running. Although it's generally inadvisable to disable system apps, as it may cause confusing issues down the line, it seems to be the only solution to get this app working.
So it appears to not have been Play Integrity after all. Which I consider good news, even though the app is weird. I still think it's a mistake that it's detecting the presence of an accessibility service and blocking access to the app even when the accessibility service is not enabled. I'll be filing a bug report with them about this.
[deleted] Thank you for sharing with me the worry about the safety of my money with this bank. Although my money in the bank is protected by Norwegian regulations which will cover losses up to 2 million NOK (or whatever the sum is now) for losses in deposits caused by a bank's negligence*, I am considering to never actually take advantage of their services. I currently have a total of 0 NOK invested with them, so the imminent danger is not large.
I'd be happy to receive banking recommendations by DM, though.
I'll stop my off-topic ramblings in this thread now.
Note that I'm not speaking as an expert. Just a random person on the internet.
*Don't take legal advice from a random person. Look it up yourself if you are in need of this knowledge.