Allow auto-refresh timespan to be greater than session length

Is your feature request related to a problem? Please describe.
Problem is that if the session length is shorter than the auto-refresh length, the update manager will never check for updates.
For example, I have set my auto-refresh to check for updates every 5 days, since I don't want to check in every session. But I shut my computer down every night. The result is that I have to check manually for updates since the auto-refresh never runs.

Describe the solution you'd like
Mintupdate should be able to keep track of when (date/time) the last update was run, regardless of whether the user has logged off or the computer is shut off. Once a new session is started, mintupdate can check to compare the last update time with the current time, and if it's greater than the auto-refresh timespan, then check for updates.

Having this will allow people to check every n days or every week for updates even if they shut their computers down in between. This approach will be more user-friendly as frequent updates can become tedious and annoying for some users.

Describe alternatives you've considered
I attempted multiple variations and combinations of settings in Auto-Refresh without success.
I have asked in multiple support forums to find out if this was just a configuration issue on my part. It was confirmed that the timespan set in the Auto-refresh setting has to be within a single session or it will not work.

Additional context
This is still an issue as of Mint 21.1

Start by tracing mintupdate's auto-refresh behavior and how the current session-based interval is evaluated. Review where the last update check could persist across logouts and shutdowns; done means a new session compares that timestamp with the configured timespan and checks for updates when the interval has elapsed.