I really liked the theory I saw few days ago in a post here.
It's the social networks lobbying for age gating, because it turns out that when internet is 90% bots, advertisers don't want to pay you as much. Why would they, if out of the 1000 reported and paid for impressions, 900 are bots?
So they started lobbying for age verification, because then you can mostly guarantee that you are advertising to real users.
I think there already was a thread with pretty in-depth investigation about who's paying for the age-verification lobby (it was Meta, trying really hard to push the responsibilty on OS instead of them having to deal with it), and it makes perfect sense.
And TBH I trust that lobby of corporations at risk of loosing profit is way more feasible reason than goverment being organized enough to realistically limit speech. It's very probably about profits first, the rest are just casualties.