Speaking as someone who has a purely theoretical understanding of parental productivity. I would say that it’s possible to use ideas like batching when you have children, but the efficiency is going to be lower than if you didn’t have kids. But because your time is much scarcer, minimal gains can still be very valuable.
Most of the successful examples I’ve run across have been people using batching and productivity systems to make the time they spend away from their children more productive.
An interesting exception I remember is a family that taught their children that if they needed to signal for attention while their parents where talking. They should hold their parents elbows, and the parent would acknowledge they understood by placing their hands over their child’s hand. That way the parent could break the conversation at a more natural point and swich contexts more smoothly.
Rest/Recovery days is a wonderful framework, one that will replace my current system of designated “autonomy days” and “obligation days”. For me I categorized days around agency, how much control did I have to choose tasks and which order I did them in. Which worked wonderfully when I chose wholesome tasks, but would go poorly when I chose too many insubstantial activities.