Mac mini storage discrepancy after deleting large video file

Those Storage figures are eye candy that can not be trusted. Instead, check the free disk space via Disk Utility.

Also, you are using Final Cut -- did you let it import footage to its project (by default at ~/Movies) or was that footage only referenced from an external disk maybe? And did you let Final Cut by default create largish ProRes media files or did you disable that in its prefs (I recommend doing that unless you are using an old Mac that stutters without that help). But anyway you can delete those ProRes files to re-gain disk space with no ill effects (I am on another Mac right now so I can't access the FCP menu to do that).

And additionally in an APFS volume duplicating a large movie is very fast and takes (almost) no disk space, so deleting the duplicate releases no disk space either.

FYI, bad things can happen if you completely run out of Free storage space including being unable to delete any files to make more room due to how the APFS file system works (Apple didn't implement any safety buffers originally....not sure if they added any later on).

If you are using Time Machine and/or some third party backup software, then any files you delete may still be retained within the hidden APFS backup snapshots. Those APFS snapshots will be automatically deleted at some unknown time in the future once those snapshots have been transferred to external media.....for TM that is usually somewhere between 24-48 hours, for third party backup software it may be sooner or even much later depending how the app is configured. You can view & delete APFS snapshots by using the information in the following Apple article, but be cautious about deleting them if they have not yet been transferred to external media.

View APFS snapshots in Disk Utility on Mac - Apple Support

Also, your boot drive appears to only be 250GB in size.....that is extremely small for editing videos. You need to be very careful to never let the Free storage value dip below 20GB or better yet 20%. Ignore the "Available" storage value since it is very misleading......with macOS "Available" is not synonymous with Free. Unfortunately the only place where you can actually find the Free storage value is in Disk Utility or the Apple System Profiler. The Free storage space value is the most important storage value.

Did you empty the Trash on the MM and restart the computer in Safe Mode to clear some caches?

To learn how to do a Safe Mode restart please click Safe Mode.

When doing a Safe Mode restart if you use an Apple wireless keyboard, plug the charging cable into the keyboard and the back of the Mac when executing the restart. Continue to hold the Shift key down until the computer fully restarts. Then restart normally and re-test.

To do that, restart the computer while you press the Shift key at startup. It'a good idea to do this process periodically as the OS also does some repairs on itself. Finally, you should also know that the only way to get an accurate result of the HD's usage is by using the Disk Utility app.