In my experience, the idea that JWT is stateless is wrong. When your client log-out you will need to keep the token in a blacklist and check all requests against it to make sure it is not reused until it expires.

Since you need to keep a list of invalid tokens, it's not easier to just use standard token. If what's you like in JWT is the ability to store a payload that your backend gets back, you can keep that in your store alongside the token and read it at the same time you check the token is valid.

IMO, JWT only makes sense when an other entity is doing the authentication of your clients.