I don't think that's particularly puzzling. While many of them are likely simple hypocrites, there is the position that the government's job in the market is to enforce the minimum amount of regulation needed to maintain a 'free' (as in competitive) market, in which framework a push for government to step in and regulate social media is understandable due to network effects being particularly relevant for it.
Personally I would agree with the argument that Twitter (and Facebook, Reddit and Youtube) are too big to not be regulated into behaving more responsibly at minimum. They're microcosms compared to the real world, but they're big parts of the internet world and thus influence many people's lives heavily, especially young people and especially over the past 2 years.
Currently it's standard practice for social media platforms to have content policies that intentionally avoid providing specifics on unacceptable content, many of them also avoid telling users exactly what the offending content is and don't offer any way to seriously appeal decisions. I think this is responsible for the vast majority of these free speech complaints, people are effectively left to assume the worst, which is extremely irresponsible for companies so large.
We see these frequently on HN too, where someone had their twitter or youtube account banned, are assuming they've been censored for saying something about the company and can't get in touch with a responsible human to find out. Usually they're just forced to start over with a new account.
Thus, I think the fix would be regulations on content policies of sufficiently large social networks that require the policies to be more well-defined, require the specific offending content to be shown along with the exact policy violated and requiring the availability of an appeals process which at least eventually reaches a human.
It might also be worth requiring some amount of disclosure on the automated moderation system's performance (ie how many automated takedowns happened and how many had to be reinstated upon appeal).