He actually doesn't own both companies.

He largely owns X which is a private entity. He owns ~20% of Tesla, and the rest is owned by other shareholders. As a company officer he has a fiduciary duty to act in the interests of all Tesla shareholders, and any sales or deals to other entities he has in an interest in pose a conflict. That conflict can often be mitigated by oversight or deferral of decision making to parties that don't hold the conflict such as other board members or corporate officers.

Tesla is a publicly traded company with shareholders.

Twitter is Musk’s private plaything.

Tesla using Twitter services could be a conflict of interest because Musk is CEO of both and could be using his position at Tesla to funnel public shareholder money into Twitter, aka his pocket.

Other shareholders of the companies might bring up conflict of interest concerns, if the deal is lopsided one way or the other.

Theoretically it is a way to siphon funds from one company to the other if he forced one of his companies to take a raw deal from the other. If both sides got a fair deal, it’s probably not much to worry about though.

He owns a fraction of Tesla and a much larger fraction of X, so there's a financial incentive to pump money and reputation from the former to the latter.

no, but there is potential so its probably better off not doing it. but this sounds pretty low for a major company's advertising budget and pretty low in relative amounts to be worth risking doing corrupt things.