I’m also getting this (Background worker disconnected) on an iPad any time the iPad screen locks, and the iPad subsequently is unlocked. Happens whether I am using the “add to home” method or just vanilla Safari. I do have several media tiles that are pointed to HTTPS mjpg streams that are visibly timed out and not refreshing, along with this (despite having the option set to refresh them).
Edit: pressing the reload button that shows up next to it refreshes everything, if this pop-up notification simply just automatically refreshed everything without presenting the pop up to the user, that would seem to avoid the problem entirely?