Seems to be some different behaviour regarding updates (for me anyway)...currently on 2023.20.4.1 and as of yesterday (July 13th) the car hadn't checked for updates since June 28th (preference set to 'Advanced'). It's been connected to the mobile network all this time (as proven by live traffic) but not wi-fi. In the past I always got notified an update was available either in the car or via the app, occasionally noticing it on TeslaMate, at which point I moved the wi-fi extender to install the upgrade.
Something different seems to be happening now, thought maybe it's not checking for updates unless connected to wi-fi but just connected it and the car still last checked in June.
But, I'd expect TeslaMate would know an update was available irrespective of whether the car is connected to anything, or asleep, as presumably it communicates directly with the server.
Very odd, but doesn't seem like I've missed much.