Safari is hard to limit as part of normal Screen Time app limits, as it doesn’t appear in the lists of apps to select. Presumably a deliberate decision on Apple’s part. This means that if you have, for example, a 2 hour limit for your child, you can’t include Safari in that limit. You can limit the individual websites that can be accessed, but not Safari itself – but this is, frankly, pants. However I found a way to include Safari as part of the total 2 hour limit, and I note that I didn’t find an explanation of this anywhere else on the web (that actually worked) so I’m documenting it here!

• In the “daily usage” section of Screen Time, find Safari (assuming it has been used in the past day) and click on it, then “Add Limit…”
• Set a limit – e.g. 2 hours – and back out.
• Go to the top-level “App Limits” page, and you’ll see a new group containing just Safari that has been created.
• Add all the other apps we want to limit into that group (games, social, entertainment etc. as per your whims).
• If you already have another group with a limit (the one you were trying and failing to add Safari to originally) then be sure to delete that in favour of your new one.

Now we have Safari included as an app in that total limit.