Return problem for Connection Error: timeout exceeded when trying to connect

Currently this error does not have explicit handling. Better might be to add explicit handling, and return a `Problem`.

E.g. `503.1 Could not get database connection from the pool`.

It is probably only helpful to add explicit handling for the case of an empty connection pool rather than e.g. a timeout connecting to the postgres server.

Start by locating the connection-pool error handling and the code that constructs API Problems. Determine how to distinguish an empty connection pool from a timeout connecting to PostgreSQL. Done means an empty pool returns Problem 503.1 with the requested message, while PostgreSQL connection timeouts are not given this handling.

Written by the indexing model from the issue text.