AVCHD import doesn't work

According to this Apple document the AVCHD format is compatible with Catalina: About incompatible media in iMovie for macOS - Apple Support

Therefore there may be something wrong with either your library or user account. To test that as a test launch Photos with the Option key held down and create a new, test library.  Try to import some videos and test to see if the same problem persists. Does it? (This tells us if the problem is limited to your current library or is more wide spread)

Next log into another user account, Set up users, guests, and groups on Mac,  and see if the problem persists (this tells us if the problem is limited to your user account or is system wide).

Lastly boot into Safe Mode (How to use safe mode on your Mac - Apple Support) by booting with the Shift key held down and check there to see if the problem persists.  Reboot normally and test again.

NOTE: Safe Mode boot can take up to 10 minutes as it's doing some system cache cleaning, volume verifying and directory repairing. 

Have you run any "cleaning", "optimizing", "speed-up" or anti-virus apps on your Mac?

A note on AVCHD: This format was developed for people who are shooting to edit the material afterwards. If you're shooting to edit, then iMovie or Final Cut are a more appropriate home for this material. If you're not shooting to edit consider using one of the other video formats on your Camera. 

That camera also shoots MPEG-4. Very high quality at modest file sizes. perfect if you're shooting to store. And if you're trying to put this in Photos and iCloud, then you're shooting to store. Why are you shooting AVCHD? And no, it wasn't working perfectly with previous releases. you said so yourself.

I've given up on AVCHD at this point. While I don't use Photos the way you use it for long term storage of AVCHD, when editing in FCPX at the end of last year, artifacts/glitches are visible at random spots. This happened a couple years ago with an FCPX update and got fixed a few months later. So, yes, functionalities break occasionally when upgrades happen. And not just with video formats. All sorts of things get broken when an OS or program is updated. My memory of this from last time is that it was more of an OS rather than FCPX issue, but it may have been fixed with an FCPX update. I just don't remember.

I searched the release notes for FCPX and the last time AVCHD was mentioned was for 10.4.1 back in April of 2018. That may have been around the time things fixed themselves. The release notes don't mention what I experienced however.

My suggestion for the long term is that you'll need to find a camera that records in 60p in mp4 format. Depending on the camera, the tradeoff with mp4 is 4GB max files that will have to be stitched together. Quicktime can do this, but I've had mixed results with a dropped frame at the stitch point. That is most likely due to the camera, not QT.

If I import these clips into FCPX, then I don't see any dropped frames when combining clips. This is using both a DJI OSMO Pocket and the Parrot ANAFI drone. Your results may vary, but from what I've read online, FCPX seems to handle this fine. I haven't edited mp4 files from these two in couple months, but they worked fine late last year and earlier this year. I've switched to using my iPhone 11 Pro for almost all video. The iPhone doesn't break up videos into 4GB clips.

Like others have suggested, Photos isn't really the optimal way to handle this (storage vs. future editing). You may look to iMovie or other video converter software for importing and then use it to covert it to mp4 to be saved in Photos. It's a kludge, but probably the only way right now. Unless Apple's new MacOS update from 5/26/20 has fixed it. No mention in the notes about AVCHD, but you may want to try it.

Other than these suggestions, I'm afraid there isn't an easy solution.

Unless you plan on doing some heavy video editing in iMovie or Final Cut Pro you probably would be best served by recording in the more compatible format.