Neat! Do you know if this works well across Spaces? I went with the wallpaper approach because I figured it was likely to be the least error-prone, especially across OS updates.
I'd point out, however, that when I first made Artpip (https://www.artpip.com/) I rendered backgrounds using a desktop level window but the performance overhead was too high when compared to just setting the backgrounds natively, so I ended up switching over to that instead. Artpip is made with Electron though, so if you do everything natively then maybe you'll see different results.
NSWindowCollectionBehaviorStationary | NSWindowCollectionBehaviorCanJoinAllSpaces
By the way, I meant to say that your approach is super cool too, and the blur and shadow effects look great.