You use the word regimented like it's bad. For me, it helped a lot.
I always 'aimed' to get out of the house, every day, by 9.30am. Walk, library, garden, anything that was free in the area.
That meant I could be back for 11am for snack. It just gave me structure, which helped.
Then quiet time and lunch. Nap time. Suddenly, the day is half done.
I'd think of some activity for the afternoon.
As loads of people have said, he can 'help' with the tea. Mine used to have a pan with dried rice and a wooden spoon. They 'cooked' tea with me.
When you are playing with him, you are 'teaching' him to play. This will help him learn how to play on his own. Mine loved (and I mean loved) threading pasta on a piece of wool with a bit of sellotape on the end.
When they were a little older, I would get them to colour in the pasta. It's not big massive, instagram worthy activities, it's little ones that help the day go quicker. If I was cleaning, my little one had a tiny broom and I would ask her to clean up something I had already put on the floor with the broom. We had some chunky wooden bead things that she liked tidying up.
Sometimes, having something planned in advance helped. Also- a 50p pot of bubbles was always popular. 20 mins frantically popping bubbles = very tired child.
When I changed the bed, I would pretend the sheets were too heavy and I needed them to help me carry them. That resulted in at least 8 trips to the washing basket, carrying super heavy sheets and pillowcases while I was actually changing the bed. Again, nobody writes about these boring things on Insta/Mumsnet but with a little planning, it can help.
And if I was too tired, that was fine as well. It just meant that gradually, I built up a bank of things I could think of doing with my toddler.