This is an idea that will never come true. First, Elon Musk is unlikely to want to create a stablecoin for Twitter as well. It won't be of much practical value. But then Elon Musk will have a lot of problems. Zuckerberg failed with his Libra/Diem stablecoin precisely because he wanted to connect a pervasive social network and finance. The states saw in this the concentration in private hands of significant confidential information about a decent part of the citizens of the planet. And this is a huge influence and power. Therefore, the states used their leverage to prevent this from happening. The same will happen with Elon Musk. He must understand this.
This thought experiment is not for questioning "if" Elon will do something like this or not. This is more about assuming he did it, and then starts afterwards and the question is would you support it.
I think it's not going to be something I can trust, dude is a weirdo and I do not trust people who act like that, it's better to be investing into something where I can see the owner as predictable, like Jeff Bezos is an asshole but at least he is predictable, he will do whatever he can to make a profit. That's why it's going to be not so easy to trust Elon, because he is unpredictable, and I do not want my money to turn into dust one day because he said some weird stuff.