After doing some research today it seems there is no way to block the Files app using Apple’s Screen Time settings. Even when the entire device is locked at Downtime, there is no way to block the Files app. Chlidren can therefore use the Files app at any time of the day or night to:
I suspect this also means that time in the Files app isn’t tracked as part of the Screen Time time limits.
Some restrictions still apply despite this fairly large loophole:
This seems like a pretty big gap in Screen Time to me. If you care about this and happen to know anyone at Apple you can prod, I’ve filed Feedback 11953747.