usability: current error log can not easily tell whether the auto analyze is killed by out of time window

## Enhancement

As you can see, the error log can only tell us that the analyze was killed by a kill signal. But you will need other logs to check whether it's killed by `max_execution_time` or `time window of the auto analyze`.

This error log will now trigger an alert in Cloud. So we may need to refine it to reduce the fake alarm.

Start by locating the auto-analyze kill logging and the related max_execution_time and time-window handling. Done means the error log distinguishes these causes clearly enough to reduce false Cloud alerts.

Written by the indexing model from the issue text.