SRE here, that's a ton of pods and sounds like it's language or architecture if you are serving up so few requests per pod.
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.
Our workloads are served by Go processes, so quite lean. But the workloads are relatively CPU-bound and memory-hungry.