#1 is a problem with the client's code, I don't know any easy workaround. Usually a long-running transaction means you're accidentally waiting on stuff like RPCs in the middle, or maybe doing something that doesn't really need to be in a xact.

#2, shouldn't the client<->PgBouncer connections stay open?

#3 is why I just use client-side pools instead of PgBouncer, but that gets annoying when you have a replicated service so you have to think about the sum of connections across all pools, so I get why people use PgBouncer.