27" iMac with LG 4K secondary display (USB-C). BigSur 11.0.1
After overnight display/system sleep, secondary display desktop "sometimes" comes up displaying only the default Big Sur graphic. No windows. Yet the windows (Safari, Terminal, Finder, etc.) exist - ie, I find them listed under the appropriate application Window menu. In some cases, where windows were on the main screen (iMac), they exist and are visible. Those that are missing had been present on the LG secondary display. Selecting such a window in the Window menu, only brings up the windows that are on the iMac (ie, windows that were originally displayed there). Terminal windows were missing but not all.
Finder was missing 6 of 8 windows. Moreover, safari only shows 1 of 2 windows that were visible when the system went to sleep. Console.app main window not found anywhere - but Window menu lists it.
Restarting Finder (Force Quit via Activity Monitor) recovered all windows - yet they were ALL displayed on the iMac - none were restored to the LG display.
Restarting OSX fixed the missing Safari window; Terminal only came back with ONE window - but I actually think that is a separate issue, cuz I"ve observed in the past that all its windows do not seem to survive a restart; only one is displayed
This issue was also observed during Big Sur Beta testing - but its "random" nature frustrated any attempts at reproducing.