In theory, there are mathematicians working with cryptography systems (no relation to cryptocurrencies, cryptography is a vast field and the rest of it is very useful for everyday life) could invent a scheme where you can prove your age without leaking any metadata to either the website asking, or the government that verified your date of birth and identity at some point in the distant past.

In practice, most implementations will be utter shit, and leak details everywhere. If someone does propose a good solution, the public won't have the expertise, or even willingness to read the specification and think critically about it to tell the difference, and will rally against both good and bad solutions alike. Except the bad solutions will be forced forwards more fervently by people poised to abuse them, so any reasonable one is all but guaranteed to be shot down.