Effective Parental/Self Control Solutions for Android?

I don’t know; but I would be surprised if that is the case.

After all, this solution is a way to overrule depending solely on self-discipline.

If the waiting periode for overrule is long enough, then its resistant against impulsive behavior

Sure. And if your need/reason to unlock before end of time is that urgent, this is probably not a solution for you.

Its not very important, cause if I there is an emergency that requires to open the box, I could probably force open the box with a hammer or something similar.

Would still nice to have something like a secondary opening method

Instead of making stupid laws, the government should support software that allows parents who want to regulate their kids to do so in a effective way.

Can DNS blocking be used when a VPN is active?

If you’re on Android yes Private DNS overrides a
VPN
MacOS also allows you to override a VPN dns via a mobileconfig file but from my testing it’s inconsistent

But then problem you then have to worry about is other browsers or whatever apps own DNS based solutions

if you’re on iOS sadly no. You have to depend on your VPNs implementations for custom dns which only iVPN has a good implementation or a custom wireguard file

Im not sure about Windows or Linux as I have not used them in a while

Can Immutable distributions solve this?

Immutable distros often prevent changes to system files.
On this regard, SecureBlue is probably the best distribution

There is no cryptographic enforcement and its trivial to get persistence as an attacker. Simple example: modify systemd service files.

No Linux distro is as secure as Android, especially with GrapheneOS