Well, again, it isn't exactly a Star Trek knockoff. Both Space Force and Star Trek were copying 1960-Present US Space Program seals. It is common inspiration, and Space Force frankly has a better claim then Star Trek.
That said, the more I think about this, the weirder it gets. Absolutely no announcement or acknowledgement from any DoD source, just thrown on Trump's twitter feed in the middle of a Friday afternoon with no fanfare. The Military LOVES ceremonies. They have ceremonies for everything, we will have a 2 hour ceremony to rename a maintenance shed, with rehearsals the day before. The military isn't going to want the symbol that represents an entire branch to be rolled out on a Page where the pinned image right now is this one:
Yes, that is a meme that Trump has pinned on his official Twitter feed while announcing the seal that will sit next to the Seal of the Army, Navy, Marine Corps and Air Force.
There couldn't be a less military way of handling this.