> Transferring your age and a way to verify it to any third party is by definition a privacy violation.

No it's not. Unless...

> Doing so in a safe way is literally impossible since I don't want to share that information in the first place.

...well then it is.

But it's not constructive to claim that proving your age to someone is by definition a privacy violation. If someone wants to prove their age to someone, then that's a private communication that they're entitled to choose to make.

It is true that if technology to achieve this becomes commonplace, then those not wishing to do so may find it impractical to maintain their privacy in this respect. But that doesn't give others the right to obstruct people who wish to communicate in this way.