My baby is now 4 months old and still wakes 3 to 4 times at night. How much sleep does my baby need at this age?

Every since my baby was born he's been a very good sleeper! At the hospital when I had him the nurses would tell me to wake him up every two to three hours which I did. So at home that was what I would do and he wouldn't really want to wake up because he was sleepy. So my mother in law told me to just let him sleep as much as he wanted. So when he wakes up he eats and is wide awake for an hour and falls back asleep. He wakes up around 7 am goes back to sleep around 8, 8:30 am wakes up around 12 pm and goes back to sleep like around 3 pm and wakes up like around 4 pm and falls asleep then wakes up like at 6 or 7pm and falls back asleep like at 9 or 10 pm and won't wake up till like 4am😱 then he eats and falls right back to sleep! And he won't wake up till like around 7 am or 8 sometimes! Just before when the baby goes to sleep if the baby is breast feed rub his little feet so he can eat more and so his tummy gets full and for bottle feeding give him an extra ounce or two more. That is what I did and it helped