Conflicts of interest?

Probably a few.

The fact that Elon Musk has his own space interests, is indeed somewhat of a conflict, but at the same time the government has no legitimate interests in competing directly with privately owned or publicly traded businesses.

DOGE to examine NASA payments
NASA’s acting administrator says DOGE will be examining payments at the agency but that safeguards are in place to prevent conflicts of interest.

That’s not what government does, and it’s certainly not Trump’s intention to gut the U.S. space program, given the establishment of the Space Force during his first term in office.