As far as Musk 'looking near to tears' when saying that it's 'difficult' to manage both his businesses and DOGE, I highly doubt he was anywhere near tears.
Musk, like all grifters and narcissists, is a consummate actor. He will portray glee or grief according to whichever of the two emotions serves his needs.
Will he quit DOGE voluntarily? I don't think so. I think he is deeply enjoying, and probably addicted to, the feelings of power and control that being able to order mass firings and the shutting down of departments wholesale gives him. In the past he's done similar to just about every company he's acquired. Why would he give up the biggest doses of his personal heroin that breaking a democracy is giving him? If he goes, it'll be because he's forced out.
And would Scrotus, who craves the attention and approval of those richer and more powerful than him, force out 'the world's richest man'? Nope. Hopefully, DOGE can be voted out of existence after a Blue Wave at the midterms. But until then, I'm afraid we're stuck.