In 2024 (maybe before) the Start Tile positions are stored in

HKEY_CURRENT_USER\SOFTWARE\Microsoft\Windows\CurrentVersion\CloudStore\Store\Cache\DefaultAccount$de${GUID}$start.tilegrid$windows.data.curatedtilecollection.tilecollection\Current

where {GUID} will vary-- look for the $start.tilegrid... suffix.

The Data value contains the Start Tile information.

Unfortunately this value is binary, but you can export the version you want and restore it. This works fine for a GPO when a user will sign in later.

If you manually restore (import) the Data valuse to a signed in account, the user has to use the Task Manager right-click menu for Windows Explorer to restart explorer. Explorer will read in your changes when it restarts. If you change the start menu by moving or adding tiles before you restart, your imported Data registry value will be overwritten.