If u feed food with lots of water content within it, yes then they wont drink much.
Don't feed too much carrots though, its very sweet and no good for them if u feed too much. Give lots of hay instead. I notice my rabbit drinks more water when he eats more hay. He usually drinks water during the late evenings.

Btw, when my rabbit was less than 5 months old, I used to give water through the bottle, now he has a water bowl. When he was young he didn't know how to drink wlfrom water bowl.

And yes, rabbits eat a lot. They need to continuously eat to keep their intestinal tract working. If there is a blockage they will die.
Feed more green vegetables and hay. Check online for a list of safe/unsafe foods for rabbits.

hi, you might need to bring your rabbit to the vet.
Noticed your rabbit having some skin problem here (paw & nose)
(if losing some fur it's okay, but the skin is reddish)

my rabbit had this problem before, kind of flaky and reddish and fur loss..
and it turns out to be mange.
treat it earlier would be better

good luck ya~

hi, you might need to bring your rabbit to the vet.
Noticed your rabbit having some skin problem here (paw & nose)
(if losing some fur it's okay, but the skin is reddish)

my rabbit had this problem before, kind of flaky and reddish and fur loss..
and it turns out to be mange.
treat it earlier would be better

good luck ya~