Welcome to the forum
My first impression is that the plant is dried out — the leaves look like it had been in the sun after cut or uprooted and deprived of normal supply of water for too long. Do you know how much roots it has? Was it given to you in the pot?Mint is pretty resilient and might still be saved, but I think most of those *leaves* are past ability to recover if they are papery and brittle. I see you have been trying to water them, but if too far gone, they will only get wet and rot.
Whether you consider them safe to eat is up to you, but if you do, then trim them off , rinse pat dry, and allow to dry out completely to use as dried herb or tea. Discard any that are discolored/blackened.
I would cut all stems back by about 1/3. For insurance/back up, keep the least shriveled, fleshy of these cut off square stems, trim off all dried leaves, and put them in a jar of water of about 2 inches/5 cm deep. Replace water every day and see if they will grow roots and new leaves.
The pot with the hopefully recovering plant should be put in shallow pan of water and kept filled. Place away from any direct sunlight but under good artificial light bright enough to read tiny print. This is a temporary care measure.
Tell us a little more about the compost. Also the holes in the leaves — were they not there before? If the holes are new, we have to assume a pest has hitched a ride.