"Struggles to wake up" is not an excuse. He is being lazy. Everyone struggles to wake up when they have young children.
I'm worse for it than my husband: very much not a morning person. But I drag myself up when it's my turn and pop a quiet tv programme on, nothing too boisterous. The night before I set up some toys in what they call an "invitation to play" for nearly 3 year old which keeps him occupied a while. We do toy rotation to keep everything fresh and interesting. Then I plonk myself on the couch with a cup of tea until I wake up enough for us to have breakfast.
Your husband needs a serious talking to. You're pregnant for Christ sake. My husband works freelance too and doesn't behave like this. He does the majority of the mornings with our toddler.
You also need to pause the masters. There will be a way to do this. I paused a diploma during maternity leave and picked it up again afterwards. You have way too much on your plate.
As for when baby arrives, it's good that you've got your older child in nursery. Do they have a summer club? Or are there any summer clubs they can go to a few days a week? I know some mums who use childminders who are nursery staff that do childminding on the side for extra money- a good way to find a babysitter who you already know and trust.
If you can pay for a cleaner or laundry service, do. I would simplify as much as you can at home regardless. So, before baby comes have a big clear out and declutter. The less stuff you have in your house, the easier it is to keep tidy. Be ruthless.
Then split chores fairly and stick to it (you should be taking lighter chores or no chores while you are heavily pregnant and post-pregnancy while you are recovering.
Simplify your cooking right down. Literally while you're in the trenches just rotate the same few meals 99% of the time. We rotate the same slow cooker meals constantly. If you have room for a chest freezer somewhere you can go mad bulk cooking soups, curries, chillies, etc and freezing them to make like easier. I've never used one but maybe one of the meal/recipe subscription services would suit you. I prefer slow cooker and freezing meals but do what suits your life.
Your number one priorities need to be having a serious word with your husband and pausing your masters. You're on the path to a nervous breakdown.