Partner not waking up from his alarm

My partner has been suffering from depression for the past 1,5 years. One of the side-affects of both the medication and his condition is that he can never get enough sleep to feel truly rested. He was a fairly poor sleeper before and this has only gotten worse. We also have a 1,5 year old baby but I have taken care of her every bedtime and night for her entire life so he’s not waking up with her in the nights, but the responsibility of being a parent obviously takes its toll.

My partner is with our baby from 6-7 am, when I try to sleep to make up for the wakes during the night. I then get up, make breakfast for myself and our baby and get ready for the day with her as my partner goes back to bed.

I start work at 8 am (I am working from home) and 80% of the time I have to go and wake up my partner so that I can get ready for work. He then takes 5-10 minutes to wake fully. Even if I leave our baby with him she walks off and he stays in bed so I look after her to make sure she doesn’t injure herself at the same time as I’m trying to get ready. It rarely works and I start work at 8.20 and with a feeling of resentment. This isn’t working for me any more.

I don’t want to have to wake him up. He’s an adult. He sets alarms and then sleep through them.
I want to set a boundary about me not being responsible for him waking up, but I don’t know how to do it. Please help.