Keep postgres logs

Currently we build everything from scratch per run. So the postgres logs will also be gone. It will be useful to keep the postgres logs at some place so that later we can connect to the cluster and see postgres logs for each run.

No files or tests are named. Start by locating the per-run PostgreSQL cluster lifecycle and teardown handling, then determine where logs could be retained per run and how a later connection would find them. Done means PostgreSQL logs remain available after each run and can be accessed for that run.

Written by the indexing model from the issue text.