The defining feature of the privilege is that it's arbitrary. If it was governed by a set of consistent rules, then it would be less effective at making him feel like he had power - the system, rather, would have power instead.
Twitter is very small compared to the likes of Google though, so not very big. It doesn't make sense to break up such a small company that basically just does one thing.
More informatively: Trump was in favor of eliminating Section 230 protections for Twitter after they fact-checked one of his lies about election security.
Presumably he will now want to revoke Section 230 for non-Twitter companies.
Trump supports people who make him feel good and hates people who make him feel bad. He isn't pointing the DoJ at big tech. He is pointing the DoJ at people who make him feel bad. Trump thinks that YouTube (and Google more broadly) is unfair to conservatives and is full of whiney liberals.
You won't see consistent application of Trump's DoJ. It'll just be a hammer that he can swing at things he doesn't like.
It could even be the case that many of the things that he swings the hammer at will deserve it. But there will be similarly deserving people, groups, and organizations who get off scot free because Trump isn't personally angry at them.
Trump is not particularly in favor of anti-trust policy in general, but he (and the GOP more generally, though Trump’s personal angle that of the GOP more broadly are slightly different though in general alignment) are very much for punishment of anyone in the information space that isn’t actively tilting in the direction he prefers, and is absolutely in favor of using antitrust law as a lever for that.
