GPT-5 says that now its not. So while lampreys are technically fish under traditional definitions, modern evolutionary science places them as one of the most primitive branches of vertebrates—not part of the “true” jawed fish group.

Only a fool would trust the output of GPT-5 for, well, any purpose.

I don't know where it got that idea because I only see a few people using the term "true fish" and they're using the normal definition of vertebrates. If you want to be extra restrictive then there's multiple options. If you really want to exclude tetrapods you might use rayed fish. And there's also bony fish if you think sharks aren't quite right having only cartilage. Who uses jawed fish in particular?