And you don't understand the purpose of JWTs.
No one needed to mention anything about stateless authentication because enabling stateless authentication is the purpose of JWTs [1].
Yes, just store a signed cookie with a random token for the session and use stateful authentication. That fits most people's needs better than stateless. (Even signing is more or less optional in many common cases. If the cookie is only a sufficiently long random token for the session key, then I don't really care if a user changes it, they'll only log themselves out.)
[1] - https://jobs.zalando.com/tech/blog/the-purpose-of-jwt-statel...
No one said anything about stateless authentication. If you're going to use cookies, and I recommend that, you need to put something in the cookie, cookies don't magically implement authentication for you. If for some reason you're not using the framework's way of authenticating with cookies, I'd recommend using JWT. Is there something else you'd recommend? Just use cookies is a hand-waving answer in and of its self.