From your first link:
Majorities of Democrats (52%), independents (59%) and Republicans (77%) all agree they have political opinions they are afraid to share.
In fact, there have been shifts across the board, where more people among all political groups feel they are walking on eggshells.
The survey finds that “cancel culture” goes both ways. Nearly a quarter (22%) of Americans support firing a business executive who personally donates to Democratic presidential candidate Joe Biden’s campaign. This share rises to 36% among strong conservatives who support firing Biden donors.
All of these quotes suggest that since Trump has been in office, fewer people are willing to share their political views for fear of reprisal. Leaving aside 1A rights (the government isn’t stopping anyone from expressing their views) I don’t know whether it’s correlation or causation but it certainly seems like the political climate has gotten more hostile since 2016.
Time will tell whether that changes if Biden becomes president. If his presidency were to somehow signal a social reaction to the coarseness of the current administration, perhaps it would be less about free speech and more about a general desire to see a return of civility in public discourse.