Blender wouldn't paint neither face sets not the mask anymore I got blender into a somewhat strange state after I decided to add some vertex colours to my sculpt for better visibility.
As I load the save file I cannot paint the face sets anymore, not can I paint the mask. 'Invert mask' would do nothing.
Creating a new mesh and trying to sculpt it won't work.
Effectively, I'm forced to go back to my older save, or copy everything to a new document.
I think the only things I did to get here was:

set up the vertex paint material
tinker with the viewport display to show vertex colours
actually paint some over the mesh

Any advice on how can I force the document back into an usable state?
Note 1: Here's the blend file featuring the problem.
Note 2: The overlays are indeed enabled.
The problem is the Armature. Modifiers prevent Hide, Mask, and Facesets in Sculpt mode. Usually, you get a warning like this:

Armature, Cloth, and Hair/Particles, and all the other physics are also Modifiers. It's probably a bug that Blender doesn't warn you if you have one of these 3 activated. (Dynamic Paint gives you a warning.)
To see your Facesets and Mask in Sculpt Mode again you just have to disable the Armature modifier in viewport render by clicking the little icon that looks like a monitor.

Make sure your Faceset overlays are enabled. It's not enabled in the uploaded blend file ;-)