Replace it. A cracked jacket is a warning.
Yes, even if you can’t see copper. That crack will flex, dirt and moisture will get in, and one day it’ll arc or short when you least expect it.
Extension cords get bent, stepped on, and dragged around. A crack in the outer jacket means the insulation underneath has already been stressed. You can’t see internal damage until something fails — usually with a spark. The cost of a new cord is like ten bucks. The cost of a fire or a fried appliance is way more.
Don’t be the person who saves eight dollars on a cord only to burn down the garage. Buy a new one, cut the ends off the old one, and use the wire for something low-voltage. Or just throw it away.
This is not where you save a few bucks.