> my guess is that states are simply copying each other and/or global conditions are similar enough that they naturally come to the same conclusions around the same time.

I think that's the wrong guess. Even with chat control, in some previous forms, the proposals came of the back of lobbying. One such case was Ashton Kutcker's startup https://www.ftm.eu/articles/ashton-kutchers-non-profit-start...

The more recent proposals for chat control were drafted by non-public "high level groups", the identity of which wasn't revealed to the public https://mullvad.net/en/why-privacy-matters/going-dark