Twitter is not private, at least from the platform discussion point of view, anyone can see Tweets even without having an account. It's more akin to modern day digital town square.

Twitter is private from the point of view that matters at hand; that is, the legal one. Whether or not you can see content without an account has no bearing on this as this is a matter of ownership and liability. Even if it did, you cannot participate in those discussions without an account.

Laws pertaining to free speech do not apply here, as has been established time and again, partly because, like I said, it is their free speech in the wider gamut to remove things they don't want. Twitter's right to free speech exists in the public space, but your right to speech extends as far as Twitter's terms of service.

This all seems mostly disingenuous anyway -- the bias is very exaggerated. The right is mostly backed by armies of bots (a violation) and generally people who flaunt the rules more (anecdotally). Just something else to be outraged at.

Ok, fine then wait and see new legislation that will be put in place soon to regulate these social media monopolies.

If that is the case, then so be it. At least that would be the correct way, even if I disagree with it. These are in no way monopolies. You have an enormous amount of choice when it comes to where to post whatever it is you want to post, regardless of whether anyone follows you there or not.

It's private in the sense that the servers are privately owned and therefore the owners should have the right to decide what goes on there.

Counterexamples:

Suppose a phone company (Verizon, Sprint, T-Mobile, etc.) decided to scan your speech for political content, then degrade your phone call quality if the algorithm decides that you seem to oppose the lobbying efforts of the company.

Suppose a package company (FedEx, UPS, DHL, etc.) decided that political items for one party would simply be destroyed, with the tracking number disappearing from the system. When you order a box of lawn signs for Biden, they never show up. Alternately, the packages aren't accepted for shipment, or they arrive with deliberate damage.

That's the private sector. Is this the world you want?

Yes. Telecom is not completely private sector as they are regulated as utilities, and for good reason.

Courier services are pretty much private entities that have liability due to the fact they do not own the things they are delivering (this is a really nuanced topic). Lying about the practice and doing it transparently would be different stories.

I don't think social media is as nuanced. If you don't like it, go start your own or use one of the many that do not censor legal content. The burden of reproducibility is very low.