6 month old sleep worry

My baby is almost 6 months and is a pretty good sleeper at night. He used to go to bed around 730pm and would wake up once to eat around 3-4 and then back to bed until 7-730. But now he is sleeping past that feeding until 530-6am. So now I am confused whether I should get up then to feed him and put him back to sleep or he should just wake up at that time. This morning I let him sit in his bassinet until he started fussing around 630 and then fed him. He played for like 30 minutes and then  fell back asleep in his bouncer. Of course I tried to move him back to bed and he fully woke up again. So should I just immediately feed him and put him back to sleep? I feel like he is not getting enough sleep overall including his daily naps. He naps for like 20-30 min each time every 2 hrs. Seems like he is probably getting like 12-13 hrs sleep a day where online it says they should get 14-15 hrs. Any suggestions? Is this a problem?