Upgraded mac OS Mojave v10.14.6's App Store keeps offering updated iMovie (v10.1.14; 12/10/2019) in standard accounts.

There’s probably another copy of iMovie residing somewhere (else) on this Mac. Run a Spotlight search. The Mac App Store uses Spotlight to find apps and versions, which means an old, “spare” copy of an app can trigger the upgrade prompts.

Common? Not that I’m aware of. Safe Mode rebuilds various caches, and disables various and potentially problematic add-ons. Between that Safe Mode rebuild and the inherent reset of most any reboot, it’s a fairly common sequence for trying to clear oddities.

Upgrading rebuilds caches, yes.

Upgrading does not remove apps, unless those apps are stored in very odd spots, or are tied into a specific version of macOS rather more tightly than might usually be preferable.

The three apps you cite very likely all involve kexts, which means ties to versions, which means app upgrades.

I’m not sure whether the reboot cleared the iMovie upgrade notice reported here, or if Safe Mode cleared it.

You’ll eventually want to avail yourself of go64, as that’ll help with the next hurdle to be encountered here, with the next upgrade.

Reboot through Safe Mode, and see if that clears this?