Yes, You could do a fight on any other sector and all combos in other sectors are changed(sometimes are staying the same combo on the exact same sector), I am using this since 2019, very usefull.
This doesn't apply to negotiations as far as I know(not entirely sure), I am not a big fan for negos, but I did remember goods requirements aren't changing on other sectors If You win a fight or a nego.
So that's it, I expected the negotiations to be changed after a fight, and not after a negotiation )))...
Also negotiations only change negotiations, and fights only change fights.