Database connection pooling: PgBouncer vs application-level pools

we're hitting a wall with database connections in rds postgres. we have around 50 microservice pods, and each maintains its own connection pool, maybe 20 connections each. that quickly adds up to 1000 connections, which is bumping against our rds instance limits and causing contention. we're evaluating solutions for better connection pooling. pgbouncer is the classic choice, but its transaction mode has some limitations for our use case, and it adds another component to manage. rds proxy is amazon's managed solution, which sounds great in theory, but we haven't benchmarked its performance or seen it handle our specific traffic patterns. what are people's real-world experiences with pgbouncer versus rds proxy at scale? are there other application-level pooling strategies or configuration changes that have helped reduce connection count effectively?