The idea that Twitter is a "public square" was recently popularized purely to create the argument that it should be owned and/or heavily regulated by the government. The imagined goal of this is for Twitter to somehow no longer have a moderation policy and only follow by the first amendment.
The idea that a company with an audience of hundreds of millions should not be able to impose its own bias on its users dates back at least almost a hundred years with utility service policies. I highly doubt this was invented overnight by the government.
This is just not a solid argument. Let's replace Twitter with the US government. Why should it be allowed to impose its own bias on billions of people worldwide?
One problem with this argument (and there are many) is that we assume that this _global_ public square should be controlled by the US government. That doesn’t make it much more fair or impartial than the current ownership. If being gay is illegal in many parts of the world, should people from those countries be able to call for punishment and basically harass gay people? If not, why not if this is a global public square.
