JWT is not a solution for that, any regular token fixes this problem. If you need something like that you can build an auth server, and everybody talks to auth server. I've built these kinds of systems, they are complex and working on them is not fun, you have to be really careful not to mess things up and if I have to worry about JWT as well, this is one more problem in a distributed system that if I can avoid, I would gladly.
TBH, I've not found use case for JWTs, maybe I'm not experienced enough and if it's there, there must be a use case for it. But I've found that there are simpler authentication schemes you can do, and I try to do them instead of implementing JWT.