To Destiny241, mingoslkd, bailier, and SnickZ—Just today, I called Apple Support and had a long and fruitful discussion with a gentleman who introduced himself Andrew. His first question was about software and have I missed any updates. Well, wouldn't you know that I had an update pending to macOS 12.6.9. I'd just checked for an update two days ago! (I ran the update after the call. It did not change any behavior in Photos. Oh, well ... .)
Andrew did the remote thing with my laptop, and together we ran through all the behaviors that I've described in this thread. I showed him that I had created a new library and that I could edit a video I'd imported into that new library. He had me import that same video into my System Library. (I had exported one of the offending videos to my desktop, and I imported from there.) So now I'm in my System Library, where I have two copies of the same video sitting side–by–side. One is the original, which entered my library the usual way: via iCloud. The second copy entered when I imported it from my desktop. The original won't let me edit it and displays the "Unsupported Video Format" error; the copy allows editing and does not display the error tag.
Neither Andrew nor I understand what's behind that phenomenon. His next suggestion was to delete my iCloud library (my System Library) and reconstitute it. Andrew showed me how to do it, and I plan to follow his advice soon.
I'll take this opportunity to praise Apple Support, to include this Community. I've dealt with support from other organizations, and I can say that nobody else comes close. I was on the phone with Andrew within two minutes of my clicking the "call" button. Andrew proved to be patient, very familiar with his product, and attentive to my concerns. He allowed me all the time I needed to discuss my problem. We didn't actually "fix" the problem with this call, but Andrew showed me what I need to do to fix it. This experience with the Community and with Apple Support reinforced my decision to stick with Apple products.