## Problem
Currently, we only report the timestamp of the last moment we think
Postgres was active. The problem is that if Postgres gets completely
unresponsive, we still report some old timestamp, and it's impossible to
distinguish situations 'Postgres is effectively down' and 'Postgres is
running, but no client activity'.
## Summary of changes
Refactor the `compute_ctl`'s compute monitor so that it was easier to
track the connection errors and failed activity checks, and report
- `now() - last_successful_check` as current downtime on any failure
- cumulative Postgres downtime during the whole compute lifetime
After adding a test, I also noticed that the compute monitor may not
reconnect even though queries fail with `connection closed` or `error
communicating with the server: Connection reset by peer (os error 54)`,
but for some reason we do not catch it with `client.is_closed()`, so I
added an explicit reconnect in case of any failures.
Discussion:
https://neondb.slack.com/archives/C03TN5G758R/p1742489426966639
