Should I be doing more?

I have a son who is almost 4 weeks old.

He feeds well, he's 1kg over birth weight, he naps during the day and has some wake windows. We are sometimes able to get him to sleep in his basket too.

At night, its a different story. My husband and I have taken to looking after our son in shifts because he won't sleep in his basket.

I exclusively breast feed, and I'll go to bed around 9pm. My husband will come and wake me if our son is hungry but usually, I'm able to sleep until midnight uninterrupted especially if our son is sleeping. He will only sleep on our chest at night so my husband will sit downstairs with him.

At midnight, I'll get up and take over so my husband can sleep as he has work at 7am.

My son will usually wake around this time and cluster feed or at least want to feed over a long period of time (few hours) Around 3am the past few nights he's been passing out. I've tried placing him in his basket and he'll sleep for 20 minutes (on a good night) but then he'll wake up, be unsettled for ages, want to feed again and will take a while to settle again to sleep.

Whereas if I let him sleep on my chest, he'll sleep until 6am or 7am.

Yesterday night, I only tried to place him in his basket once as I was too exhausted to keep trying and found it easier to just watch TV whilst he conked out on my chest.

Now its almost 3am again and he's finally passed out after 3 hours of feeding and fussiness. I'm not wanting to place him in his basket since I'm just relieved he's finally sleeping and am too exhausted to settle him if he wakes during the basket transition. I will try in a few hours when I've recovered a bit and my nipples aren't so sore but am I just being lazy?

Should I be trying to place him in his basket all night and just deal with the wake up if that happens?