I don’t know what this “collusion” is. Companies with common ownership often cross-bill and this is used as a vehicle (search “transfer pricing” if you want to know more) to move profits around and optimise tax. There are restrictions on transfer pricing, but there’s no concept of collusion here and in particular there really is no restriction related to fair market rate. There are lots of ways to do the billing part of this which would be perfectly normal.
It’s a terrible idea because it’s a nasty way to treat people at the acquired company and probably ineffective at getting any useful information, but Elon Musk has shown that he doesn’t have many scruples about that sort of thing.
But SpaceX, Tesla, and Twitter don't really have common ownership in the normal sense. They're not owned by the same holding or parent company, they're not owned by the same single person, one is public and two are private, etc.
If Tesla engineers are spending time on something not beneficial to Tesla but instead to Musk personally or to X Holdings, that's absolutely something Tesla shareholders could sue for.
No they couldn’t. Fiduciary responsibility doesn’t mean you have to only do things that shareholders agree with. It means you have to act in good faith to represent their interests.
In this case Musk could easily say he had spare capacity, and if there’s crossbilling (which can happen retroactively if there was an objection) there’s really nothing to sue over. If he can get tesla engineers to try to build a cave rescue submarine to buff his public persona he can get them to do this.
As I said, I don't believe any significant TSLA holder will actually sue Musk. It's clear by now they're comfortable with Musk's view that his interests and any of his companies' interests are equivalent. But if they did, they'd have a good case unless Twitter overpaid (at which point the issue would be any Twitter shareholders).
It’s a terrible idea because it’s a nasty way to treat people at the acquired company and probably ineffective at getting any useful information, but Elon Musk has shown that he doesn’t have many scruples about that sort of thing.