So, your question supposed to be ‘Get notified while the service stopped’.
Should not be as ‘Feature to auto-restart of mysql while it down with reasons’.
To get alerted for mysql service, currently no feature yet on hestia & many branded leading panels also will not let us to have this feature by default [alerting only]. The reason is the alert feature is not guaranteed.
Let say, if server down, email service down etc.,
I set a 3rd party service, which will just keep monitoring my essential ports & alert me if it down.
in your case, you have to find what is that break point, which is stopping your mysql.
Also set some scripts to ALERT you only. Dont auto-restart. As SysAdmin people, they knows well why im saying this.