2am feeding schedule is destroying my brain

My son is 3 weeks old and we're still doing the every-2-hour feeds. My wife pumps and I bottle feed at night so she can sleep, which sounds great in theory, but I'm absolutely losing it. I've been up since 11pm and have feeds at 1am, 3am, 5am scheduled. The worst part is the 3am one where he takes forever and I'm just standing in the kitchen half-asleep trying to burp him. Anyone else feel like they're in a zombie apocalypse? When does this actually get better?