You don't need the ID. You can simply store the token's signature. In fact, some implementations store the whole JWT to avoid roundtrips to the auth service, and revoking the token is just a matter of flipping an attribute in the database.
The token expiry determines the baseline accuracy of banning across all services.
JWT and sessionIds are totally different beasts. JWT are used per request, are designed to expire and be refreshed, are specific to each individual endpoint and store authorization info in a specialized third party service.
But either way, if you really can't afford a database or cache layer lookup to see if a token is still valid, then you accept that by using a bearer token, that is only validated by signature alone, that it is possible a user will have their session hijacked without possibility of revokation.
The usual way this is mitigated is by use of a small expiry time (I've commonly seen <=5 min) and a revokable refresh token. This still gives a hijacker a possible 5 minutes (assuming 5 minute expiry) if a user revoked the refresh token, but it does mitigate the damage while still reducing DB lookups since you only do a lookup in token refresh. Hope that clears things up. Again your application needs should drive these decisions.