Always interesting to hear other perspectives on simple stuff like this. Personally, I like doing dishes in the morning while the espresso machine heats up. It's a nice rote task my half-asleep brain can come up to speed on, I feel like I've accomplished something right out of the gate, and I didn't need to interrupt the flow of whatever I was enjoying the previous night.
Oh... what I mean is, one of the things that is interesting about the gap between the two sleeps is that your brain is awash with prolactin.
So some tasks you do in that period of time are done with a kind of lower level of objection, easier "starting", and in a contemplative start, and you're not actually tired.
Which is what also gives this "cleaning fairy" sense that nobody in particular did it.