Follow baby cues or fix a routine

Hello mummies! First time mummy here and I feel overwhelmed with things I read about managing every stage of baby’s growth online. My baby is 3 months old and I read that his routine should be drink milk > play 30mins > nap. Sometimes he is awake and wants to play after drinking milk, sometimes he is yawning after drinking milk. When I see that he seems tired, I try to pat him to sleep but he would cry quite badly for about 1-3mins before falling asleep. Is this normal? Does it mean he does not want to sleep or he is overtired? Should babies nap without struggle? I’m worried if I’m not picking his cues right or is it because I’m not playing with him enough to tire him out? Should I stick strictly to routine of milk > play > nap or follow baby’s cues? And on some days if I follow his cues and he seems sleepy all day, I feel like I didn’t ‘play’ enough with him and am afraid it will affect his development? I feel so confused and disappointed in myself that after 3 months I still can’t figure out my baby’s cues, understand wake and sleep windows :(