I’ve never seen lights like that, I imagine that translucent plastic is simply to let daylight in. Probably switched out the front door at one point and couldn’t find one the exact width so got a narrower one, filling in the gaps with that translucent material. I wouldn’t think the switch would have anything to do with it. Sometimes people just remove a light and don’t want to bother taking out the wire and switch and changing the box and patching the drywall.
Personally I don’t think you would need the tape. It’s usually for the gaps between sheets of drywall which can be significantly wider than these cracks. You should be fine just filling with the drywall compound and sanding.
For this you might end up seeing the thickness of the tape beneath the new layer of paint afterwards.