I know most of this affects only the US, but I'm wondering where this will go in the EU if the Age Verification Tech goes ahead in America. There's been lots of efforts to increase surveillance disguised as protection for kids in the EU and UK.

The Swiss implementation of eID may be hint that governments may/will take the responsibility to implement and maintain the tech, but the multiple intrusions and lobbying by Palantir and friends in the EU gives me the ick.

The EU, unfortunately, has shown to be very susceptible to this kind of lobbying in the past. We regularly see legislation that is being rammed and rushed through in spite of vocal opposition. I would be very, very worried. (EU citizen)
What examples of this do you have in recent years (post 2016)? The clearest example of lobbying (chat control) has repeatedly been struck down.
"repeatedly struck down" means somebody keeps bringing it back
They're proposals by a minority. I'd like to see it go to see chat control go to grave permanently, but I'd also rather not that the democratic system allows for the permanent barring an impossible to define class of proposals from even being proposed. Or do you have other solutions?
I'm definitely for creating EU directives that enhances digital privacy rights and sovereignty to block whole classes of privacy-endangering surveillance proposals in the future. That seems like the best solution to me. It's much better than allowing those proposals to be made again and again until they are passed in some shady package deal. Even if such a proposal is struck down by local laws, constitutions, or the ECHR, once they have the foot in the door, they will only be modified minimally to comply with the constitution.