This isn't a given. It is quite possible to build a reasonably anonymous system to verify age at signup.
As a simplified model: the government creates a website where with your government id/login, they will give you an age-verification-valid-for-5-minutes token - basically just "holder is 16+" signed with their signature & the current time. Websites request a new valid token at signup. End result is that government only knows you're _maybe_ doing _something_ 16+, and the website doesn't know who you are, just that you're old enough (this is clearly improveable, it's just a basic example).
Whether anything like this will be implemented is a hard question of course. The current alternatives I've seen seem to be a fully privatised version of this, where a private company has a video call where you hold up your ID - that eliminates the government, but seems like a whole bunch of privacy concerns in itself too (not to mention being wildly inefficient & probably not very reliable).