Did a delete and repost to correct the title.
I'm thinking their next step will be pressuring web hosting providers to dump websites such as this one as clients. A example of this happened in 2019 with some low hanging fruit, 8chan (now know as 8Kun.) They tried to link the Christchurch mosque shootings with 8chan, pushing the narrative that the shooter was radicalized on 8chan. They claimed this was so by claiming that the shooter originally posted his manifesto on 8chan They sucessfully got Cloudflare do stop providing DDoS mitigation for them and got a web hosting provider or two to dump them.
I can easily see them pushing the false narrative that sites such as thedonald are radicalizing people to become white nationalists that want to destory democracy, promote hatred, promoted racism, etc. and that no "respectable company" should provide any services for them with threats to bridage them on places such as Twitter if they don't comply.
Edit: A comment on the uncorrected title post mentioned trying to go after DNS records as another vector of censorship.