Update applied by hand, how to tell App Store app? Net is slow at my home, really slow. It would have taken a week to get Xcode 12.4, so instead I got the package from Apple onto my laptop elsewhere, brought it home, transferred it over, and installed it. Worked great, I'm currently using it.
But the App Store app thinks it still needs to be updated. Is there a way to tell it what's up?
If it’s working I would leave it be until the next update. Fiddling with a signed app can make it not run.
I would recommend getting content caching on your slow network. You can even take that storage and Mac to a fast network to get the App Store apps cached to an external disk and bring that cache back to the slow network. Subsequently  when you update at home, the update comes from your local network cache and not Apple. New bits come in incrementally and update the cache until old apps age out when storage pressure grows and forces out the old bits to keep the freshest ones cached.

https://support.apple.com/guide/mac-help/set-up-content-caching-on-mac-mchl3b6c3720/mac

The iCloud caching is also a huge benefit for slow networks. We use these at work extensively. Instead of 50 Xcode installs, only one downloads and the rest are cached locally.