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Android has this in the app manifest, but of course Google doesn't expose this to users

Are they're any ROMs that do?

I used to be able to on ArrowOS, LineageOS and I think on MIUI. Its been a few years since I gave up on custom roms though, so it may no longer be the case.

On Android it is typically done with a firewall app, like AFWall+

GrapheneOS does

Every app you install with Play Store pops up and asks if you want to grant it networking. It's cool

Little Snitch is the best I found although not perfect. (Apps can trivially bypass filtering)

iOS has a "Local Network" Setting for some apps, e.g. VLC, PhotoSync.

That's for apps that request the additional ability to poke about in the local network to look for e.g streaming devices or other devices to control