I'm a developer with LetsMove integrated into my app SelfControl. In macOS Big Sur, you can turn on "Downtime" or other app limits using the Screen Time. In this case, affected apps have their windows taken over and show a "Time Limit" screen, with some buttons allowing the user to ignore the limit and continue.
When opening my app during Downtime without LetsMove, it opens fine (shows the Time Limit screen, and can be bypassed using the Ignore Limit button). With the LetsMove dialog enabled, the app still shows the "Time Limit" screen but the buttons aren't clickable. So there's no way to bypass the dialog and continue. It looks like it's some sort of window focus issue.

Ideally, LetsMove would work seamlessly with Screen Time and the buttons would be clickable!