Well on the "far beyond free speech advocates", the position that the SEC can't prevent market manipulation due to the first amendment is a position that basically no one sensible takes. Or that he's happy using "Free Speech" to slander people.
On the subject of Twitter being a public square, I think that's a pretty absurd assertion, it's one of a plethora of social media sites - Facebook, Youtube, Instagram, Whatsapp, Reddit, Tiktok, Telegram, Snapchat. And it's not even particularly large compared to that competition. It's not even like Twitter has grown to become some behemoth, it's share price is about flat over the last decade. This isn't some behemoth that needs regulating.