The server tells everyone who could open the old path where a file or folder
went (checked before folder settings change, so restricted names don't leak),
and clients re-point their tabs through ComfyUI's own rename without a second
server move. Tabs of files moved out of reach stay as private copies.
Replaces Share this tab / Stop sharing and the auto-share settings. The Live
list shows workflows someone has open, the Files tab marks live files,
private tabs offer Move to Shared, and deleting or moving a live file into a
private folder closes its room on the server.