Halo Master Chief Collection won’t install on pc and also says I have an update for MCC when it’s not even on my pc

In the end I solved it (at least for me, check out if it works for you as well).

I had the impression the game didn't install because in some way, even if I had the downloading drive for new applications set as the one with the most free disk space (D:), still the Store was actually trying to install on C:.

So I did the following: first go to the advanced settings for the Microsoft Store app and deactivate the option for making it run on background. Then open the Store app and cancel all pending downloads for Halo. Then go back to the app's advanced settings and click on the button to kill the process, then click on the button to reset the app. If for any reason you're prevented from taking these steps for some kind of error, restart the system first.

Then go to Settings > Storage and click on "Change Where New Content Is Saved". Now for me, when I opened this windows, everything was already set to D:, but in my opinion that was a plain lie. So, for the option regarding new apps, I switched to C (and clicked Apply) and then back to D (by clicking Apply again). Now at this point it might be that you'll see the classic Window's loading circles circling like for ever. If it does, still wait something like 30 or more seconds, then click on the Back arrow, and go back again to the "Change Where New Content Is Saved" page. You should see that the option for new apps is D again.

So now that theoretically the drive where to save the apps is REALLY set to D this time, open the microsoft store, select MCC and start downloading it (better not to select one of the single games that are part of the package, but you're free to try. Just to be sure I preferred to download the entire bundle).

That's it, hope this will help you!