Can I install a second layer of drywall on my bathroom ceiling to refresh the surface?
I don’t see any problem, with multiple changes I believe it is a better way to go. Even using an electric blower to move cellulose when I pulled it down there was still a mess. The others we did were overlays.
In a bathroom is 1 place I suggest using hot mud or setting compound for those new to Sheetrock. Hot mud is affected less by moisture than standard mud. Get the 1 hour stuff not the 15 minute and when it starts to set, toss anything that's left in the pan and mix a new batch.