If the use of their account meets certain legal criteria which make it a limited public forum, yes; that's generally true of official government accounts, whether of an office or office holder, but can be true of notionally personal accounts if used for government purposes (as the court has evidence, including White House statements, was the case for Trump's “personal” account.)
Note that while Trump's Twitter account is the highest visibility case on this issue, there have been a number of similar cases regarding local government offices and officials accounts on various social media platforms with the same general result before the case about Trump's account was filed.
The peculiarity of this case is more that Trump’s thin skin and refusal to understand how the First Amendment applies to him.