> I think I’ve seen movement on the tiles in its task switcher, so I’m not clear if it takes screenshots.
In my experience, it seems like only the app you were in when you brought up the task switcher continues to update the screen. If you go somewhere else, like just back to the home screen, it goes static like all the rest.
This is correct. iOS snapshots the app as soon as it's moved into the background, and that snapshot is what you see. When you bring up the switcher, the foreground app isn't backgrounded yet — that only happens if you go to the home screen or actually switch apps.
If the app is using the Background App Refresh entitlements [1] (Background fetch / background processing) then it is possible for iOS to update the screenshot for the app switcher periodically even when the app is in the background
Messages does this, as you will notice that an active conversation tends to be up-to-date in the app switcher
In my experience, it seems like only the app you were in when you brought up the task switcher continues to update the screen. If you go somewhere else, like just back to the home screen, it goes static like all the rest.