How long do you let your kids entertain themselves for?

I have a 15 month old son and his sleeping routine is a mess. My husband and I keep him on a schedule but despite our efforts he falls asleep anytime from 9pm-12am šŸ™„šŸ¤¦šŸ»ā€ā™€ļøšŸ˜© so the time he wakes up in the morning is always different. Sometimes he will wake up at 6am, sometimes 8am and sometimes 10am. I want him to get enough sleep and be able to function during the day so I let him sleep until he naturally wakes up. Anyway..... on the days he wakes up early at 6 or 7am I just let him play with toys in my room or he lays with me in my bed and watches a movie until I wake up at 8. I feel like the worst mom doing this but Iā€™m pregnant and chasing after my son and cooking and cleaning and playing all day so I need my sleep šŸ˜©. Do you have your toddlers entertain themselves for an hour or two at a time so you can keep your sanity? Or should I start the day when he decides to? Just feel like Iā€™m doing everything wrong. Open to suggestions that might help.