It's not yet known if Trump and the Justice Department will try to escalate the appeal, although that appears likely. The White House has maintained that Trump's personal account (the one he uses most often) isn't covered by the First Amendment like an official account would be, and that muting Twitter users wouldn't be sufficient.
The case originated in 2017, when the Knight First Amendment Institute sued on behalf of seven Twitter users who Trump had blocked. They argued that Trump's account is a "public forum," and that blocking them prevented them from not only responding to the President's claims but from reading his statements while logged in. They also contended that the blocks prevented others from seeing political dissent in Trump's replies, creating an "echo chamber" where free speech is suppressed.