The comparison is difficult.
Putin, Xi etc. have heavy-handed controls over state media and Xi of course total control over social media. The US is not 'headed in this direction'.
'Free Speech' is the wrong banner for this discussion, as no-one's speech is threatened here - everyone is essentially free to say as they please publicly, and on their own web sites.
The Press is 'free' to say what they want, which includes a ton of bias, but that is what it is.
'Social Media' is a very new thing - it turns out it can be extensively influential and 'memes' from out of nowhere can grab narratives like dogs chasing each other through a crowd.
FB and Twitter are private platforms, concerned with content unlike AT&T, Amazon, email or network providers who are fully neutral - and Social Media has always been censoring content: if you attack individuals or threaten violence etc. you would have been banned 10 years ago.
The algorithms have always been favouring one thing or another using any variety of criteria, so the very nuanced question boils down to the nature of 'truthiness', the degree to which it can be assessed, and how much it can be used for algorithmic purpose - and especially, how could it be done 'fairly'.
I wonder if there are truly objective methods whereby people only ever see posts if they are shared directly by friends, thereby implying a more 'direct' model, like email, whereby if one party wants to chose with a specific, other party, well there's nary anything anyone should censor there.
Alternatively, one could contemplate anything with any political content whatsoever, to be in fact, political, and to be managed in accordance with the same rules for political spending etc. - but that might be altogether too much.
I honestly don't think that this is an existential question to the point wherein industries need to be disrupted or transformed, we are probably 'somewhere near' reasonable at this point, with some modifications we may have a system we can live with.
Finally - it should be noted that 'free expression' doesn't in any way imply 'fair expression' - like a free market, it can be leveraged and dominated by a few small voices who want to 'take control'. There's no reason that a few smart minds couldn't establish control over the narrative whereupon we'd have to ask ourselves if that's what is remotely good for society. As much as we sometimes loathe the press today, there are a lot of checks and balances, along with 'narrative driven news' the MSM are beholden to mostly facts, there's quite a lot of integrity in that system. A 'free for all' wouldn't have any such controls and any kind of real truth could be lost.
Perhaps the best solution would be to just stop using social media as we do. I did, and don't miss it at all.