Agree breastfeeding lying down! I had great support from a birth centre, they recommended feed with the breast closest to the bed (so right breast if lying on right side, left if on left side). Me and baby then learned how to do feed with either boob me lying on my right side so less disruption.
DH WFH, picks own hours but very busy. He'd do nappy changes at night, bring water, bring baby from bassinet to me to feed and put him back down after.
I built a milk stash using the haakaa and once we had enough for some bottle feeds, DH started taking our baby for bits of time at night and giving expressed milk. Even 2 hours was just amazing relief (our son was almost officially low birth weight, cluster fed extremely frequently). I then started pumping so 6 weeks - 3mo DH would take him for several hours and I would sleep - blissful. DH wouldn't let me co sleep, too scared of the risks so it was very necessary.
Then started cosleeping from 3 months, DS in solid bedtime routine, would go down for his first stretch then into bed with me. DH would have us on the monitor while he worked overnight just in case, the compromise we reached to let me co sleep and get some sleep. DH also did all cooking and cleaning!
Try and sleep if your baby will tolerate being put down to sleep in the bassinet (mine wouldn't from 6 weeks). But use some of the daytime to do things for your sanity, like go outside.
Big hugs. I'd love another one but the newborn stage was tough! That sleep deprivation was nuts.