My proposal does not give google any extra power or extra user data or even implicit trust.
I did not propose any rules. I proposed a header.
Google already creates and re-creates "the internet" for the vast majority of people on the regular basis by messing with its algorithm, pre-empting search results with AI-spam, showing ads, etc.
My statement was an assertion that the power google holds over the internet at-large is enough to incentivize compliance with opt-in content ratings for huge amounts of the web.
I also said nothing about adult search terms. The point is that an adult website can mark itself as one intentionally (X-Cotent-Rating: Mature) and then when google gets a search from a child's computer those results are simply filtered out. they already do this but site owners have no way to tell the world their intended audience.