Do such downlights exist? (downlights with motion sensors)
A quick eBay/AliEx search didn't find anything and nothing in stores either.
It would be nice to just use the existing neat power and fittings to light the front door area instead of having to pick up and add external lighting, plus req a sparky for fixed wiring ones too. The idea being wanting to avoid just external blocky solar powered ones if we can.
If you can find the plug inside the ceiling then replace the whole unit.