I really wouldn’t worry about it yet. There are so many GS when they are little and frequent feeding is a natures way to tell your body to produce more.
Perhaps you are concerned that you are relying on bfing rather than shush/pat for helping him sleep? At 3 wks I really wouldn't worry, if this is already in your mind then that's enough IMO. When we started EASY my mother would always try to re-offer the (old!) bottle when it was nap time even, totally encouraging feeding to sleep even though he wasn't crying for food or at all hungry, it's was just her way, drove me nuts of course. I felt that at 4.5 or 5wks old mine didn't need the bottle to sleep, but he did need help and it was a gradual process to teach him to sleep alone.
Thing is even if you did feed to sleep what 's the worst that happens? So you have a prop, so what? it's not for life, you can wean that at any point when you feel it necessary or you're ready.
I honestly don't think you can stop every 3wk old falling to sleep on the breast, I know you can encourage them to stay awake but there's all that sleepy hormone stuff in your milk (get me, I have no idea what it's called!) and they are tiny and exhausted from the effort to feed. When he's a bit older he will manage to be a bit more awake.
I know we all want to start off with good habits but there is massive benefit to the bonding and trust he's getting from bf. I just don't see any negative in that at all (other than you being utterly exhausted, sore nipples, never sleep etc etc etc...yeah ok there are some negatives, but not for him).