These third parties tend to be US based, as well. That always raises privacy questions due to "Safe Harbor". It was completely stupid of the government not to even provide a UK age verification service before putting this in place.
There are lots of age-verification providers in the UK / EU. The industry had plenty of notice this was coming and reacted accordingly.
"Do it intentionally" is a funny way to spell "I'm forcing you to do it by law and if you don't you won't be allowed to communicate with other humans in a digital form or access digital content".
And even then it's still a leak when the provider inevitably gets hacked and all your data is out there and you have no legal recourse to get reasonable compensation for it.