It implies that the user has access to the technical infrastructure that supports age verification. Sucks to be you, if you can't afford a recent Apple or Android device to run the AgeVerification app.
There is also the problem of mission creep. Once the infrastructure is in place, to control access to age-restricted content, other services might become out of reach. In particular, anonymous usage of online forums might no longer be possible.
The EU Digital Wallet requires hardware attestation so only it only works on locked-down government-approved OSes. That opens the door for government control of all electronic devices.
OS-level ability to verify the age of the person using it absolutely provides infrastructure for the OS to verify all sorts of other things. Citizenship, identity, you name it. When it's at the OS level there's no way to do anything privately on that machine ever again.
I agree that a checkbox for if the user is over 18 opens the door to a checkbox for if the user is a citizen and even a textbox for the user's full name (which already exists on Linux so you better boycott Debian now!). I don't see how such input fields are "total surveillance".