To put it differently, logical separation of state doesn't have to mean physical separation of state. One Postgres instance can hold your whole app's state -- just, put each service's data into a separate database within Postgres. I've done this and I like it a lot.
Well, I don't think you can have transactions open across logical databases any more than you can join across them. And you might anyway design the relevant component to serve multiple clients simultaneously, so you could still be executing multiple simultaneous transactions.
The component is the sole owner of its state. How it interacts with that state is an internal concern.