To me it feels that the age verfication (adult de-anonymisation) push, at least in Europe, is coming more from the increasingly-authoritarian left as a reaction to the rise of the online right and Musk's Twitter.
(Maybe some unspoken element of concern over social media bots, too - as they evolve from spamming copy+pasted comments to being near-indistinguisable from actual human accounts?)
It would be interesting to see a similar lobbying breakdown for the EU and UK. I bet it's still Meta with other right wing actors. The left rarely has the money for this kind of lobbying scale
If you look at the people pushing these bills it's the anti-trans and anti-porn activists. Not the left.