literally just an unmodified Unicode character. and therefore unable to be trademarked
[edit] Please also see @arborelia's followup re: fonts vs Unicode code points
I've seen it said a few times that Elon's "𝕏" logo is "just a Unicode character", but that's not the end of the story, because Unicode isn't just a bunch of platonic forms that came from nowhere.
In this case, unmodified from what? There isn't one default Unicode font. Unicode renders their charts to PDF using a few proprietary fonts, and for example they have to show CJK characters in several different fonts because they can look different in Chinese hanzi, Japanese kanji, or Korean hanja. Some characters can't be found in any publicly available font.
This example on compart.com is rendered in the Adobe Source Sans Pro font, created by Paul D. Hunt. So I believe Paul D. Hunt is the one who drew the double-struck X in those particular proportions.
Remarkably for an Adobe product, Source Sans Pro is open source, under the Open Font License. Anyone can use it. But that doesn't mean it's public domain for anyone to say "I made this".
As a geometrically simple character that fonts have no particular reason to stylize, it probably looks extremely similar in other fonts, so it may be hard to tell exactly which font they used over at the site formerly known as Twitter. But it is possible that Adobe owns Elon's logo.