That's not accurate. Copyright and trademark are two different things. The name "twitter" is also just a combination of preexisting characters and the word was probably in use before the company was founded. You can still trademark existing things because trademarks are about preventing consumer confusion, not protecting original creations.
Musk does have a problem with copyright if it turns out this specific design was made by someone else.
Not to defend musk, but it's not from one specific font. The logo is just Unicode char 1D54F, a blackboard bold X/"MATHEMATICAL DOUBLE-STRUCK CAPITAL X"
A character is nothing without a font though. When you look at a character on-screen, it's being rendered in a specific font. Typing that Unicode character in "Special Alphabets 4" produces the image in question.
The character (𝕏) doesn’t actually doesn’t exist in the font, because supporting arbitrary Unicode characters in every font would be absurd. Paste it into the font preview and it renders a black square.
If your font has the potential to be made into a logo, you would think the designer would have the sense to negotiate a higher rate. I have no idea if that's how it is in practice, but to do otherwise seems quite foolish.