Windows automatically moves my custom Snipping Tool screenshots folder into the OneDrive folder.

Your Screenshots folder is being redirected into OneDrive, which points to a OneDrive or Windows Backup folder-backup setting rather than Snipping Tool independently choosing a location. First, save or confirm that the local screenshots you need are present before changing any backup option. Open the OneDrive cloud icon, choose Settings, then Sync and backup and Manage backup; review the Pictures setting. Also open Settings, Accounts, Windows backup and inspect the OneDrive folder-sync choices. If Pictures backup is enabled, turn it off and select the option to keep files on this PC. Then move existing screenshots from the OneDrive Pictures path back to the local Pictures\Screenshots folder and confirm the folder’s Location tab points there. Do not delete the OneDrive copy until the local files open correctly. If the setting re-enables itself, the device may be managed by an organizational policy, so ask the administrator to review that policy.