No, it’s not different now because you’re conflating two different things. One is the first amendment cited in Twitter case. The other is free speech cited here.
Did Twitter violate the principles of free speech by shutting Trump down? Well he was using his speech to foment an insurrection and caused a mob to sack the Capitol so yes, Twitter, within the bounds of the first amendment, for an eminently justifiable reason (to preserve democracy), attacked Trump’s speech, which is against free speech, yet preserves free speech, because the alternative was allowing insurrection to continue. The first amendment cannot hold under a dictatorship, as we are seeing right now as all press are (were? Are they complying with the order?) illegally banned from the White House.
It’s not straightforward but it’s consistent.