Postgresql – Connection pooling with 3 databases but 1 database as master for repmgr replication

with PGBouncer, you'd probably want to just stick with NullPool. In that case you may be able to share a single Engine across subprocesses since no socket connections will be carried over the subprocess boundary. But you can't share anything referring to a Connection object, like a Session with an active transaction, over this boundary. You definitely wouldn't want to do "engine-per-request" though, an Engine is an expensive object that accumulates a lot of information about a particular database URL the first time it sees it.

I believe the answer here is "not exactly". Those stats are coming from pgbouncer itself, so that don't map directly to the postgres backends. That said, you can track connection, data, and query statistics in postgres, but the information won't align exactly, and will probably be formatted differently (ie. you're more likely to get a counter than a gauge, so you'll need to do some tracking/math yourself)