Been there.
It’s get a grip crisis time but be kind to yourself! Also, this is the worst point, it will start getting slowly but surely easier.
Formula. Definitely.
Longer between feeds. That’s what gets them sleeping longer. First a few minutes, keep building it up. A midwife told me, every time they cry for a feed, change their nappy, as that takes a few minutes, or cuddle or wind instead. This is just to alongate the time.
Cot attached to bed, the safe ones.
Pay for a sleep Psychologist.
Pay for at least 2 weeks or M&S ready meals or online shopping. No cooking or washing up for two weeks. Pay to get a cleaner for a month.
Only go out with the pushchair when the baby is awake. Everything around the baby now. So you Maximise time when they are asleep in your house. Or if it works better for you to get them to sleep out of your arms, do the opposite.
Routine every day, Around the baby. Minimise anything else. Anything.
Spend at least a month doing just what is needed, don’t force it, go with the flow, and get some energy back.
After a month, review if you can do something to help. Then go back to a month doing nothing but look after the baby again if needed.
Repeat until it gets better! Which it will!