I feel like I’m screwing up my 4-month-old’s sleep

Our super preemie baby had a long NICU stay, came home around 1 month-adjusted will some medical issues. We were just winging it for sleep, but she mostly fell asleep after every feed so we didn’t pay much mind to it. Medical issues are mostly resolved now but I feel like we are screwing up this whole sleep / wake window thing.

I try desperately to get her to sleep after being awake for 2hr+ but someone must be paying her to try to stay awake. She eats every 2-3hrs. Ideally she’ll feed to sleep, but often she’s wide awake then I move on to shush, bouncing, butt pats. If I’m desperate, I’ll put her in the carrier which sometimes works.

Often though, I’m fighting her to sleep for over an hour at which point it’s time to eat again and the cycle continues. If we go through enough cycles, she’ll crash and nap for 3-4.5 hours.

She sleeps well through the night, but I just feel like I’m screwing her up with her being overtired all the time. What am I doing wrong?