I think this is missing the point of the no-longer-free-speach-absolutist sentiment (henceforth NLFSA). You note, correctly I think, that
> we've seen a lot of egregious, potent, and dangerous lies from credible, verified institutions including the former POTUS, prominent newspapers, and other important cultural institutions.
The NLFSA notes that we've been seeing a new attack on free speech and free thought emerge, namely Steven Bannon 'flood the zone with shit' approach.
The classical free speech position is to fight bad ideas with better ideas, fight bad speech with good. We're running into largely unprecedented problems (in the anglosphere, at least) where bad speech is drowning out the good. There are many things we can point as possible causes (say the internet changing communication patterns, information siloing, propaganda, etc.) and there aren't clear solutions.
Conventional free speech absolutism prevents you from being muzzled -- but that's it. Acknowledging you can be silenced by a chorus of people shouting over you requires a new position.
> I don't know how someone can look at American politics and politicians (never mind cultural institutions) over the last ~decade and conclude that these people are fit to regulate Americans' speech.
The NLFSA doesn't necessarily want speech regulated, or regulated by the government, or by corporations. They may not have any particular solution in mind (though some might think they have one). The NLFSA sees a problem without necessarily seeing a solution.
I think it's reasonable to see all this, and despite our problems double down on convention free speech absolutism -- that being muzzled is the most dangerous form of intervention, that better speech will ultimately win out over bad ideas. But I don't fault someone for changing their mind to try to combat rampant conspiracy theories.