Thank you for taking this bun in!
My first thought is he was starving when you found him. If you feel him over, like you seem to have done, you’ll find he’s skinny, with protruding hip bones. It’d be a good idea to weigh him twice per week (I weigh my buns in a bowl on normal kitchen scales) and write down his weight. That way you can make a weight curve and see pretty much exactly how he fares. You are likely to see considerable weight gain over these next few weeks.
If he is getting more dry food from you than he’s been used to, (hay, pellets) he’ll drink a lot. This is normal and good. Keep a close eye on output -pee and poop. Ideally his poops will be big and round and plentiful. If you see a few extra cecals, it’s still normal, he’s adjusting to getting good healthy food on a regular basis. It’s wise to not give too much pellets, but you can give hay freely.
I currently have a young fosterbun who was food deprived in his former home, due to a very bossy brother. This bun is obsessed with food. Rabbits should always be “food addicts”, but this bun is obsessed.
In short, I think your bun was very lucky to have been rescued by you. Keep an eye on poop, pee and weight. Signs of good health are, for example, a shiny coat of fur, bright eyes (no discharge) and a clear nose (no thick snot).