Muhaisnah flat — the AC pipes in the ceiling are sweating and staining, is it the insulation?

That's almost certainly the pipe insulation, not a leak, which is why the plumber found nothing, it's condensation, not water escaping. The cold AC pipes in the ceiling are wrapped in foam lagging; over years in older buildings that lagging hardens, cracks or gets crushed and gapped, and once a section of cold pipe is bare, the humid Dubai air condenses on it exactly like a cold drink sweats, then drips onto the ceiling and stains it. So the wet pipes and brown patches are the classic signature of perished lagging, and it also quietly wastes cooling into the void. The fix is cheap and simple: re-lag the bare and perished sections properly, which stops both the dripping and the waste, no need to touch the AC unit itself. Getting the AC pipe insulation checked and the perished runs re-lagged is a small job that ends the ceiling staining for good. Worth doing promptly, though, because repeated wetting is what turns a stain into actual ceiling damage.