Synapse should close idle database connections

This issue has been migrated from [#5728](https://github.com/matrix-org/synapse/issues/5728).

---

It seems the database connection pooling doesn't shut down idle database connections:
```
SELECT application_name, datname, usename, state, age(now(), query_start), wait_event_type, wait_event, query FROM pg_stat_activity WHERE now() - interval '10s' > query_start ORDER BY age;
application_name | datname | usename | state | age | wait_event_type | wait_event | query
------------------+---------+----------------+-------+-----------------+-----------------+------------+--------
synapse-media | matrix | matrix-synapse | idle | 00:00:14.840869 | Client | ClientRead | COMMIT
synapse-event | matrix | matrix-synapse | idle | 00:08:34.818956 | Client | ClientRead | COMMIT
synapse-event | matrix | matrix-synapse | idle | 00:08:34.836956 | Client | ClientRead | COMMIT
synapse-cl-rdr | matrix | matrix-synapse | idle | 00:08:34.837199 | Client | ClientRead | COMMIT
synapse-cl-rdr | matrix | matrix-synapse | idle | 00:08:40.64963 | Client | ClientRead | COMMIT
(5 rows)
```

Because every Postgres process uses 150MB RSS at me, it would the helpful if Synapse could close the database connections when not needed.