I don't see why them being third party would make it illegal to put Xbox in the trailer.
It wouldn't. Its just people making excuses.
Until the deal is given the legal greenlight Zenimax management is free to do whatever they want, including which platforms to support going forwards. They are free to make exclusivity deals with whomever they choose, all they have to do is pick things that won't interfere with the goals and objectives of their soon-to-be new owner.
You'd have to be a fool to believe that in the interregnum between the transfer being agreed upon by the buying/selling parties, and the deal being legally approved and done Zenimax as a corporate entity is in a state of limbo and unable to make future-focussed decisions.
Any project announced now wont likely hit the market before 2023, so if anyone is hedging their bets its Zenimax current management team because they have to make contingency plans in case the sale does fall through. Were they to go all-in on MS right now, they'd devalue themselves to anyone but MS. The simple truth is that there are other big fish out there who have the funds to buy them whole.
Its pretty dumb not to think that Google, Amazon, or Tencent among others wouldn't be interested in acquiring Zenimax' IP to bolster their own businesses.