I've yet to definitively determine a distinguishing factor between photos I can edit on my Mac and photos I can't edit, but I have a guess. I have photos going back to 2001, which I took on my first digital camera, a Nikon E995. In 2007, I got a Canon Powershot A710. I first discovered the problem when I decided to edit a large number of photos I took with the Nikon on a trip to Italy in 2004. Most of them gave me the "Cannot start editing" error. The same was true with other Nikon and Canon photos I checked at random. Some I could edit, and some I couldn't -- even when it was a group of photos I took during the same shoot. The only possible difference I can think of is that I might have previously edited some and not others from a given shoot (I've had Aperture, iPhoto, and Photos). With the Italy photos, I made duplicates of all of them a decade or so ago and applied heavy effects with ON1. Now, those versions struck me as tacky, so I went back to edit the originals, most of which I hadn't touched before.
I've randomly checked photos from 2012 onward that I shot with an iPhone 4, 5, 6S+, and XR, and a Sony NEX 6 and a6000, and I haven't gotten a "Cannot start editing" error with any of them. So my guess is that Photos under Monterey has trouble recognizing photos taken with two old cameras I used to have, and only when I hadn't made previous edits to those photos. I don't know how I'd check for that, though. When I want to use Photos on my Mac to edit a group of old photos taken with the Nikon or Canon, my solution, since I have an iPad Pro with iOS 15, as well as an iCloud account, is to quickly go through them with Photos on my iPad, make a tiny edit, and save them. Then I can edit them on my Mac.