Had a very similar experience with a bank few years ago. I filed an official complaint because it was not possible to verify the caller was authentic.

Can you guess what happened next? Yep... The complaints team cold called me and requested PII to confirm they were talking to the right person. I refused and the call ended.

Later got a letter saying it wasn't possible to followup on my issue and they didn't see any issues with what I had raised. I tried... :/