Almost all of this seems untrue (except maybe the last one). I’ve worked at a variety of banks from front to back office across securities and private wealth. I’ve seen plenty of company-specific languages, plenty of C++, Java, perl, python but have literally never encountered a COBOL system. There’s one system at one of the banks that I was a contractor at which may have been COBOL I’m not sure. I didn’t work directly on it and it ran on a Tandem.
I’ve never worked for a pure retail bank so it’s possible that some pure retail banks use COBOL, but I have worked on settlement systems, payment systems, reconciliation systems etc including for banks that have a retail arm as part of a larger bank and haven’t seen hide nor hair of COBOL anywhere. Some cynical part of me wonders whether IBM PR or some niche trade body or recruitment agency seeds these stories into the press every now and again to get people to fixate on COBOL and these clunky mainframes being somehow essential to the financial system.