The "Tumblrgate", back in 2018, happened because Apple removed the Tumblr app from its App Store, and Tumblr had to censor its content overnight to make it return. Other sites have removed or banned sexual content because on imposition of advertisement brokers or the credit card processors used to bill users and/or advertisers. You know, when you run an Internet business, you need money to pay for servers, bandwidth and programmer salaries. Free sites depend on revenue from the advertisers, paid sites depend on revenue from subscribers.
All this happened way before the current wave of age verification laws. For example, Yahoo and Flickr banned nudes from public groups and galleries around 2010, more than ten years ago (Flickr was owned by Yahoo back then). The agents behind this change are mainly banks, ad brokers and some tech companies, like Apple. The governments, as usual, are late to the party.