I verified with Apple that all of the wallpaper-related issues with Sonoma are different manifestations the problem I described earlier. I have been working with low-level OS code for decades and this type of thing is very common, albeit most of the time it's caught during unit/alpha/beta testing. Granted, the issue(s) could've been hashed out better, but hindsight is 20/20.
Once the root cause is found (if not already), the fix will most likely be simple and it will have the appearance of solving multiple problems -- this is because all wallpaper-related features use a common set of subsystem calls. If one of those system calls is buggy, LOTS of features will appear to be individual bugs.
[Edited by Moderator]