I'm having the same problem. Pressing the Windows key opens the OS start menu instead of the Start11 one. This happens 100% of the time, regardless of what application is in the foreground.
I've discovered a workaround: I can get the Start11 start menu to come up if I press Shift+Windows. This works 100% of the time.
I'm on Windows 11 Pro build 22621.1778, fully updated. My keyboard is a Keychron K10 Pro with no keys remapped. The problem occurs under both Start11 1.4.5.0-j307 beta and the out-of-band Start11 1.4.5.1 that was linked above.
Please let me know if I can assist in helping diagnose this issue.