Agreed. It should work. Several other posters have had the same issue. For some reason, there have been lots of glitchy things with Montery 12.3. Since the Photos app is built into the operating system, that might account for it not interfacing correctly with iMovie. Or maybe it's the iMovie update that is not referencing the Photos app properly. If so, I suspect that a future Monterey or iMovie update update would cure that. Meanwhile, we are stuck with workarounds.
You might just be able to drag the edited photo from the Photos app library directly into an iMovie timeline. and have it carry over the edits. Or drag to the desktop and then to the timeline. Both methods work with Mojave and iMovie 10.1.12 that I am running. Not perfect, but a lot fewer clicks.
-- Rich