Hi James, thanks for reaching out! In regards to connection pooling, that really depends on your application.
I personally did not run into connection issues while doing performance tests in this workshop, but the operations were quite cheap.
The good part is that it IS possible with RDS Proxy, but I would only introduce it if you experience performance issues. It introduces quite a lot of complexity.
My recommendation is to test, see if you can handle spikes of 100+concurrent lambda's, and if that's no issue, just do it without the pooling.