They claim that the Biden admin pressured them to do it, except that they had been voluntarily doing it even during Trump's initial presidency.

The current administration has been openly threatening companies over anything and everything they don't like, it isn't surprising all of the tech companies are claiming they actually support the first amendment and were forced by one of the current administration's favorite scapegoats to censor things.

If you can't be trusted to police your self, then it's a natural result that others will do it for you.

Thankfully the constitution explicitly forbids that in the US.

Evidently it does not because it happens all the time. See: Jimmy Kimmel 2 nights ago as your most recent example.

Huh, last I heard was that Jimmy Kimmel is back on air.

If the Trump administration had decided to follow through with their threats, ABC could have sued and won.

Lastly, Jimmy Kimmel could have(and still possibly might be able to) sue for tortious interference.

Nexstar and Sinclair are still blocking their stations from airing him which accounts for a quarter of the US.

They're private companies. If the reason they're doing this is govt pressure (FCC licenses?), that's not ok though.

Kimmel intentionally spread a lie to his audiences for political gain. Turns out that is against the terms of ABC’s FCC broadcast license.

They asked him to apologize and he refused, so they suspended him.

That was abc, and they just put him back.