Thanks for the reply. Here is the info you requested:
1. Windows 11 Pro, Version 21H2, Build 22000.282
2. Start 11 Version 0.94 (update via "Check Now" button)
3. AMD 3700x CPU, GTX 1060 GPU, 16GB RAM
The issue didn't seem to happen for the first week or so I installed it, it just kinda happened out of nowhere. I created a GIF that shows exactly what happens (or rather, doesn't happen).

Image 1: Default state, blue button, start menu is hidden.
Image 2: Start button clicked, purple button, start menu did not show.
Image 3: Back to default state, menu flashes for a brief second.
Image 4: Start button clicked, purple button, start menu finally shows.
Edit: I should mention I have not tested with the start menu animation disabled. I just disabled it now, and the issue is not happening so far (scratch that, it just happened). Even with the animation disabled, I am still seeing a "slight" animation where it snaps into place really fast.