[lloeki]

Screen Time does that, minus the input box.

"Always allowed apps appear normally", others are grayed out. When tapped they present a fullscreen "time out!" screen. You can ignore the limit from that screen but it presents you options and requires two or three taps so it kind of "gets in the way". I presume your input box could fit in there, although personally I think I would end up filling it with nonsense, or it would always be the same.

There's a bunch of analytics, like first pick up app. I don't think there is about overrides.

It can sync across Apple devices so you can't cheat by using another one.

Combine that with home screens + Focus modes and you can get in control.

(also "apps" above can be websites too in Screen Time")