1. They lost this legal challenge, so perhaps their UK lawyers (barristers?) knew that much broader claim would be even less likely to work and advised them against it. Just because they didn't challenge the overall law in court doesn't mean they wouldn't challenge it in a political sense.
2. The Protests against SOPA and PIPA[1] were in response to overreach by capitalists, and as such drew support from many capitalists with opposing interests (e.g. Google, Craigslist, Flickr, Reddit, Tumblr, Twitter, Wordpress, etc.). Certainly Reddit et al have similar general concerns with having to implement ID systems as they did about policing content for IP violations, but the biggest impact will be on minors, which AFAIK are far from the most popular advertising demo. Certainly some adult users will be put off by the hassle and/or insult, but how many, and for how long?
3. Wikimedia is a US-based organization, and the two major organizers of the 2012 protests--Fight for the Future[2] and the Electronic Frontier Foundation[3]--are US-focused as well. The EFF does have a blog post about these UK laws, but AFAICT no history of bringing legal and/or protest action there. This dovetails nicely with the previous point, while we're at it: the US spends $300B on digital ads every year, whereas the UK only spends $40B[4]. The per-capita spends are closer ($870/p v. $567/p), but the fact remains: the US is the lifeblood of these companies in a way that the UK is not.
4. More fundamentally, I strongly suspect that "big business is trying to ruin the internet by hoarding their property" is an easier sell for the average voter than "big government is trying to ruin the internet by protecting children from adult content". We can call it fascism all we like, but at the end of the day, people do seem concerned about children accessing adult content. IMHO YouTube brainrot content farms are a much bigger threat to children than porn, but I'm not a parent.
The final point is perhaps weakened by the ongoing AI debates, where there's suddenly a ton of support for the "we're protecting artists!" arguments employed in 2012. Still, I think the general shape of things is clear: Wikimedia stood in solidarity with many others in 2012, and now stands relatively alone.
[1] https://en.wikipedia.org/wiki/Protests_against_SOPA_and_PIPA
[2] https://www.fightforthefuture.org/
[3] https://www.eff.org/pages/legal-cases
[4] https://www.salehoo.com/learn/digital-ad-spend-by-country