I have also heard about a Trump backed coin. But I don't think it has been launched yet. If it is launched, then Trump will surely try to promote his coin because he is a businessman at heart. I didn't hear anything about Elon's involvement in this so far but don't get shocked if you eventually come to know that Elon is also a stakeholder in this.

But honestly, I don't think Bitcoin is in trouble at all. otherwise you wouldn't have seen such a bull run. I think Trump has made multiple promises during his election promotion and if he starts delivering onto them, Bitcoin will be in a better position and also the crypto companies will be able to continue their businesses without fear of regulatory actions.