How to keep clingy daughter busy?

Tl:dr I'm in something of a critical moment in my career, had to take a break to help at home with newborn, and my 3 year old daughter doesn't really play by herself.

Slightly longer explanation: I'm a researcher, I got to the point that I really have to finish a bunch of projects soon (or kiss goodbye any dreams of staying in academia). My daughter is home from preschool for the next month, my wife is mostly too busy with the newborn son to keep her company or entertain her, so I'm trying to work from home around taking care of daughter and keeping the home on track at all (laundry and cooking/washing, just the minimum). The end result is that I don't really manage to work during the day, instead staying up very late or waking up at 3/4 to work, and that's not sustainable. I'm tired all the time and the stress of worrying about my work is leaking to affect my behavior with my family, though I'm really trying to keep it at bay.

I really need your best methods to keep kids at that age busy by themselves. Some games or riddles that are addictive or reward concentration in a way even toddlers notice, or any other tricks you may have figured. Doesn't need to work forever, anything that may buy a quiet hour is definitely worth a try. Obviously she's already getting the amount of screen time we feel appropriate, and would not go beyond that.