Alternating or offer both?

Hi moms! My 3.5 month baby sleeps from.7pm-4:50am so i nurse on one side. He eats a good amount since i feel my breast softening. I burp him since i noticed that hes falling asleep and then i offer the other breast. He doesnt drink out of it and instead falls asleep. Ive Been seeing people say offer one breast and then the otherand then other moms saying to just alternate the boob per feed. My question is which is correct? Do i pump the other side or wait for next feed to offer it?