My PR blender/blender#104535
was committed as 88f9c55f7f and the logic was changed
while adding support for face sets, making the logic incorrect and
the warning system disfunctional.
Restore the logic from the original PR with added support for face sets,
fix const correctness issues, improve variable naming, and remove a
check for empty names, since all attribute-type layers should have
names in a valid mesh.
Fixes #105780