There's a number of complex issues feeding into this.
Twitter did this willingly
There's no indication that the government did this by force. Twitter's Trust and Safety team willingly deleted content, limited the reach of posts and users, and in some cases suspended accounts in concert with the FBI
Taibbi also found that a “surprisingly high number” of the FBI’s missives were requests “for Twitter to take action on election misinformation,” including obvious jokes from accounts with low number of followers.
There is no constitutional protection from Twitter doing any of that. Twitter is a private company and can remove content as it sees fit.
The Big Tech/Common Carrier/Public Square debate
Prior to 2016, it's unlikely any Republican would have espoused these ideas, for fear of being labeled censorship. But then Donald Trump came along and openly warred with social media. He later wrote an executive order to that effect
The growth of online platforms in recent years raises important questions about applying the ideals of the First Amendment to modern communications technology. Today, many Americans follow the news, stay in touch with friends and family, and share their views on current events through social media and other online platforms. As a result, these platforms function in many ways as a 21st century equivalent of the public square.
Most of the executive order, however, was pure bluster. He was openly critical of Section 230 of the Communications Decency Act that shields companies that publish data from third parties from civil liability. Most of the EO focused on why Trump thought Section 230 did not apply to companies like Twitter. As EOs do not carry the force of legislation, it could not actually alter how the courts have ruled Section 230 applies.
Trump is not alone in this viewpoint. Elizabeth Warren (hardly a Trump ally) has made more or less the same claim
[Musk's purchase of Twitter] is dangerous for our democracy. Billionaires like Elon Musk play by a different set of rules than everyone else, accumulating power for their own gain. We need a wealth tax and strong rules to hold Big Tech accountable.
If Twitter were re-defined as a common carrier that would potentially change things for it
Common carriers are prohibited from discriminating against lawful goods or communications. A telecommunications company cannot treat calls from white supremacists differently from calls from a vegan, a communist, or a flat Earther. A ferry cannot deny passage to a paying customer waiting on the wharf.
This argument is novel, however, because telephone companies do not regulate the speech made over their service, a point made later in the article
But [the common carrier] analogy does not work. One of the critical features of common carriers is that they hold themselves out to the public as neutral conduits, treating all communications or goods the same. The largest social media companies make it explicit in their content moderation rules that they do not treat all content equally.
SCOTUS still views compelled speech dimly
From 2018, there was NIFLA v Becerra over California's law compelling crisis pregnancy centers (which aim to convince pregnant women not to have abortions) to provide materials to their clients about how they could obtain an abortion. SCOTUS ruled that unonstitutional (from Page 18 of the PDF)
In sum, neither California nor the Ninth Circuit has identified a persuasive reason for treating professional speech as a unique category that is exempt from ordinary
First Amendment principles. We do not foreclose the possibility that some such reason exists. We need not do so because the licensed notice cannot survive even inter-
mediate scrutiny. California asserts a single interest to justify the licensed notice: providing low-income women with information about state-sponsored services. Assuming that this is a substantial state interest, the licensed notice is not sufficiently drawn to achieve it.
Where's the line?
The line is compelled speech (i.e. "Say this or else we will levy some sort of penalty towards you"). This would include things like the FBI threatening to investigate Twitter if they don't cooperate. Courts (and the public in general) would not be pleased with that.