>I am not sure I see a fundamental distinction between HN censoring your speech on their platform or the government preventing you from speaking in public. Both are censoring you right?

Wrong. HN is not "censoring" you at all, which requires engaging in violence (or threat of violence) against you to inhibit you from speaking in public. HN is literally engaging in Free Speech itself. Take arguably the most fundamental free speech activity in a democracy: advocating to your peers for the candidate you wish to vote for and have elected to represent you. You've researched and listened to Alice, Bob and Carol. You decide the best is Alice, and to show your support you do the quintessential thing and put out a Vote For Alice lawn sign on your lawn. That's obviously free speech right? Now what if instead some volunteer from Alice's election team comes by and asks you if they can put up a sign on your property, and you say yes. That too clearly involves your free speech rights, even if you didn't pay for the sign. Now say Bob & Carol's campaigns turn up, and they ask to put up signs on your lawn too. You don't support them and say no. Have you censored them? Of course not, that's ridiculous. Free speech isn't "everything is equal nothing matters", everyone is trying collectively to iterate towards truth and value by making their cases and listening, without general use of force. To say that "I think this idea/person/item is the best choice" by definition is exclusionary, it's also saying "I think all the other ideas/persons/items are NOT the best choice". It can also simply be "I wish to engage with these subjects, not those". You can make a forum dedicated to airplanes & cats, and ban anyone who starts threads on boats & lizards. You may have nothing whatsoever against boats or lizards, but that's not what you personally want to focus on on your own forum you're paying for.

Hacker News is the private property of its owners. They have their own free speech rights. Exercising those rights is not censorship.

Others in turn are free to use their property and/or their voice on public property to make their cases, and they can try to convince you and vice versa. And there can be social consequences, if someone really dislikes your speech maybe they don't invite you to dinner anymore and urge others to do the same, who might agree (or go the other way, or just ignore it). Humans can get passionate sometimes. But by keeping violence out of the whole thing outside of narrow exceptions that undermine the approach itself, room is preserved for minds to be changed and rifts mended years or even decades later, and for ideas to come back around if someone cares enough.

Government enforcing things though always involves violence, either directly or one or more orders removed. But a general monopoly on the legitimate use of force is a defining feature of government. If government doesn't like Alice, and tells you take down the sign, or else, that's fundamental infringement. They're closing down the whole cycle (if a private person did that it'd also be a bunch of other crimes AND infringement, because private persons are not allowed to use violence against others at all by default outside of narrow exceptions). And if government tells you "oh you can leave up the sign about Alice, but it's not fair you censor Bob & Carol, you must put up signs for them too. Or else." that'd be equally infringing censorship. If everyone has a sign, it's the same message as nobody having one. It's still suppressing "I think Alice is the best choice".

>For a large part I see people using digital platforms as a primary method of expressing their thoughts and opinions.

It is easier and cheaper than any point in human history to put up your own website, including your own forum to try to form a community around. You have no right to an audience though.

>Governments in both the US and the EU have imposed restrictions on what platforms may host.

What? What restriction has government in the US imposed beyond the long standing and unchanged exceptions that prove the rule (which essentially boil down to threats of violence, comms integral to crime, defamation AFTER a court case to prove it, serious violations of personal self with zero public value like CSAM, and purely commercial speech engaging in fraud)?

>I think we have not reconciled yet how to reinterpret free speech online.

There is nothing to reinterpret. We've gotten it fine since the passage of Section 230. The problem are constant efforts to suppress what we've already got, in some cases coupled with completely orthogonal issues like failure to enforce ancient anti-trust legislation.