"Elon and the tech bros" are not part of the "executive branch." That's the whole point. We just threw a handful of unvetted, unconfirmed, unknown twenty-something hackers into the inner workings of the federal government, gave them access to terabytes of private data (including people's SSNs, confidential health information, passwords, etc) and said "go wild." Can you imagine the hissy fit you and all the other conservatives would have pitched if Biden had announced that, say, Bill Gates was going to be given unfettered access to the federal government databases to do whatever he wanted with them?
There is no need for Trump to use Elon and his hacker brigade to supposedly root out corruption. Hire auditors. Hire accountants. Have them report to congressional committees. Or - here's an idea - use Republicans' complete control of all the branches of government to pass new laws controlling government efficiency and spending. You just have the typical conservative fantasy that every bit of red tape that prevents people from doing whatever they want must actually be unnecessary and counterproductive. When in reality there is a reason the president can't just let anyone he wants have personal access to the social security numbers of every American and the keys to the bank accounts that the government uses to disburse trillions of dollars.
As for Elon himself - the man has proven himself an inveterate and unapologetic liar many times over. the fact that he's made a lot of money by capitalizing on the hard work of a lot of other people doesn't make him a genius, and it sure as hell doesn't mean he knows anything about how government works or how it should work. The conservative hard-on for billionaires as the best and most precious members of society is just hilarious. The guy didn't get to be the richest man in the world by looking out for anyone but himself or his own interests. Why do you think the Trump admin has quickly cancelled and dismissed all sorts of investigations and lawsuits relating to Musk's companies? Why do you think trump just issued an executive order pledging the US's support for the supposedly oppressed white minority South Africans? Does Elon Musk have to go on TV and announce "I'm using my position of power and influence to get rich" for you to believe it? Conservatives will spend years on obsessive wild goose chases over some minor incident of welfare fraud then ignore the most obvious corruption in the world staring them right in the face.