Hello Eric. This problem of a slideshow background reverting to a static picture when changing virtual desktops in Windows 11, is an existing limitation in the current implementation of desktop personalization. When a user chooses a slideshow as their background background style and changes to another virtual desktop, Windows reverts to a static image and disables the slideshow setting. The defaulting behavior is not configurable by the user, as this is related to Windows desktop sessions, and how Windows persists backgrounds.
Unfortunately, Microsoft has not documented this particular behavior and no known workaround exists through the Windows registry. Windows also doesn't support changing registry keys related to virtual desktops, as it is susceptible to system instability. For all background behavior to be consistent across virtual desktops, Microsoft has recommended using either a solid color or a static picture as the background as opposed to a slideshow.
Best regards,