"Stateless" refers to the app, not to its datastores, because that would be nonsensical.
JWT is also poorly specified (no protocol under any circumstances should use negotiation, it does not support revocation, and it has been hammered home by the best security folks I know that public key cryptography is what you do when you don't have any other choice) and dangerous to use. Avoid it. Do the simplest thing that can possibly work. That's a session token. If, in the far and unlikely future, you are so successful that a single database call is so harmful, then you have the money to hire someone who doesn't have to Ask HN this question.