All normal! I was so touched out when I had a newborn, and like you, my DH always suggested a feed whenever she cried (I eventually lost it at him, and we agreed that he’d always give it a few minutes of cuddles before he gave her to me, just to allow me a break!)
I would 100% give baby to a trusted adult and go sleep. I used to have my DM and MIL each visit one day a week. I’d feed baby on their arrival, and then go nap (after some pleasantries!) while they cuddled her. I used to make a bottle up for them to offer her, but once that bottle was done, they’d wake me. It still meant an hour or two of napping a day. Weekends, my DH covered the nap, so this happened more days than not.
we also did a formula feed over night. I found it so helpful - our process was at 9pm, I’d breastfeed (even if she wasn’t that hungry), and go to bed. DH would formula feed until 1am on demand (again, feeding around 1am regardless of demand in order to prolong her sleep), and then bring her up to our room and leave her in the next to me cot, so that her next wake after 1am would wake me up, and then I’d breastfeed. 4 hours (often 5 if he did a 1am feed, she’d sleep till 2am) of solid sleep was a godsend for my ability to cope with life! That worked because I naturally prefer an earlier bedtime to DH. My DB and his wife do a similar thing but reversed, so DB wakes up at 4am and covers 4-8am while my SIL sleeps.
So on an average day, DD had 3 bottles - 1 for my nap and 2 for my night sleep. I didn’t feel formula helped her sleep longer, but of course it helped me. It also didn’t impact my breastfeeding, but it did help my mental stability. So I recommend it too!
my baby didn’t go 3-4 hours between feeds until she was 9/10 months old and well into being weaned.