A cesura should apply for all instruments automatically
When you have a multi-instrument score and you enter a cesura for one instrument, the play of the score results in a time shifted instrument or in other words: a complete mess. It makes no sense to have a cesura for a single instrument only and it would be helpful to have it entered like double lines or repetition brackets for all instruments at a time.
Comments
I'm not sure that I agree that it should be copied like a repeat to all staves. I've certainly seen cases where one or several instruments pause/breathe, while other instruments hold a fermata.
However, I can say that there is no playback issue in MuseScore. (which is what it sound like you were complaining of?) MuseScore's playback doesn't continue with the other instruments until the pausing instrument goes on. MuS seems to be playing as if all instruments had the caesura. I would have expected it to play as if other instruments had a fermata instead.
Interesting! If I include a fermata over the other instruments, it still doesn't get out of synch. But it first plays the fermata (on all instruments!) then pauses for the caesura (on all instruments).
Ahh, but if a note in another instrument is tied over the caesura in the one, that note is held properly.