What's the difference between an opaque token and a cookie that has a single session identifier in it? 'y know - the way we did it in the 90's.
You could store JWT in a cookie, or use opaque token in a HTTP header, for example.
That said, the session cookies we loved back in the day were usually opaque tokens, yeah.
As sibling comments point out, an opaque token can be stored elsewhere (though, to be fair, the session identifier which is in that cookie can be placed elsewhere too).
Cookies are limited in where they can be sent (https://developer.mozilla.org/en-US/docs/Web/Security/Same-o...).