"The conversation over what is to be done is, however, ultimately parasitic on a deeper debate: Do (or should) individuals have a right to free speech on these platforms? Or, put another way: Do (or should) companies have a right to censor users and exercise complete discretion over what can and can’t be said?"
I think these are the wrong questions.
The debate between fully free speech on the platforms (which would let loose all sorts of noxious racists, terrorist recruiters, sex offenders, and the like) is a different question than "should a private company be allowed to influence the results of our elections".
It is possible to still censor the former while allowing full freedoms to the latter.
"It is surprising to see right-leaning actors looking to government action on this matter because the classical liberal view is that companies like Twitter and Facebook should be free to regulate their platforms as they see fit. "
Eh, not so surprising. The US has wrestled with this problem in the past, with the FCC and Fairness Doctrines regulating the political speech of the various private communications companies with regard to access by political actors. This is just the latest technological challenge to free access to the Public Square of Ideas.
"Philip Pettit, has circumscribed this effort around the central idea that freedom — a singularly guiding value — is demarcated not by the absence of interference as liberalism suggests, but by the absence of domination."
Although interesting, I'd suggest that Milton Friedman offers a simpler solution. He refers to what is called "neighborhood effects", wherein any organization that (1) threatens the common good, AND (b) that threat is unmitigated by market forces....in that situation, the government under conservative/libertarian principles is morally justified in regulating it.
But, at the end of the day, we agree: self-regulation is not the way to go. Biased censorship = voter suppression.