As a data point FWIW, I have operated a PG11 cluster (on RDS), client-side pooling only, with 300-450 app servers and max_connections=2000-3000 (can’t remember)

As a data point FWIW, I have operated a PG11 cluster (on RDS), client-side pooling only, with 300-450 app servers and max_connections=2000-3000 (can’t remember), and didn’t observe significant backend resource contention or performance degradation, just a memory cost linear to number of connections,