We have Kubernetes here too for Java monoliths and we have 8 Pods serving more than that. Since Java has connection pooling, the overhead has never been enough to justify overhead of Pgbouncer for this Java app.
But this is only true if you have no more than a few running instances of your application. So it feels like the cases where you must have Postgres (over an alternative like SQLite) but can't justify PgBouncer are very narrow.