Apparently the Windows 11 Start Menu layout is stored in the folder %LocalAppdata%\Packages\Microsoft.Windows.StartMenuExperienceHost_cw5n1h2txyewy\LocalState as a file called start.bin.
So adding the folder should do the trick
[IncludeFolderTrees]
<LocalAppData>\Packages\Microsoft.Windows.StartMenuExperienceHost_cw5n1h2txyewy\LocalState
