There is a solution for limp carrots (as long as they’re just a little dim, as you said, and not shriveled into nothingness.)
Anyhow, take the tallest glass you have. Cut off the root end of each carrot and place root side down into that glass full of water. Keep in fridge overnight and they should be good as new the next morning, or 24 hrs. at the most. They’ve just lost a little moisture.
This is also what I always routinely do with Asparagus as soon as I get them home since I’ve rarely found stores which keep them properly. Same thing; the root end should be freshly cut and placed in water. I also loosely place a plastic baggie over the top of the stack of them in the glass.
In order to keep flowers lasting longer, we routinely do a fresh cut on the stem end before placing in water.
It makes perfect sense to me to do the same for veggies losing moisture as well.