Database connection pooling: PgBouncer vs application-level pools

we're encountering database connection limit issues in our PostgreSQL RDS instances. we have around 50 application pods, and if each pod maintains, say, 20 connections, we quickly hit the default 1000-connection limit for our RDS tier during deploys or traffic spikes. this has led us to look into connection pooling solutions. the main candidates are PgBouncer and application-level connection pools (e.g., HikariCP in Java). PgBouncer seems like the obvious choice for external pooling, but i've heard about limitations, especially with its transaction mode, which can mess with things like session variables or prepared statements if not carefully managed. application-level pooling is fine for individual pods but doesn't solve the aggregate connection count problem. there's also RDS Proxy now, which seems to offer a managed PgBouncer-like experience. what are the practical trade-offs and best practices for choosing between PgBouncer, application pools, or RDS Proxy in a high-concurrency microservice environment?