Does LuckPerms use Redis as a message broker or as a caching system too? I want to reduce connections to Database by using redis.

It just uses it as a messaging broker. Caching is done internally.
The database connections are due to LP using a connection Pool to improve performance. Having multiple connections shouldn’t be an issue whatsoever.

It's used only as a message broker.

If you want to limit database connections - firstly make sure you actually do need to reduce them (are you trying to solve a specific problem?) - then try tweaking the connection pool settings.