@jul1a OP I’m so sorry, my LO went through this too, and finally turned a corner around 10 weeks. The sleep deprivation is unreal. I think this is to be expected in the ‘fourth trimester’ though.
I got her more and more used to her next to me crib by slowly increasing the amount of naps she had in there. I could easily reach out with my arm to comfort her if she stirred. I also placed a hot water bottle in her crib for a minute prior to putting her there, and once she was over 4kg I used a sleep sack. Both of these helped.
For her main sleep overnight I would contact nap with her for a few hours at a time, change and feed, then back to contact napping. My saving grace was my mum and MIL, who came over during the day while she was awake so I could take a 3 hour nap, and my husband who took over the majority of household chores, cooking, laundry etc so I could focus on the baby. I’m EBF so I pumped so I wouldn’t have to be awake for feeds during those times.
Now, she sleeps beautifully for 3-4 hours at a time at night between feeds, happily in her next to me crib. She’s 13 weeks so it only ended a few weeks ago, but it feels like a lifetime ago!
Hoping your LO turns a corner soon.