I read once that the carriers carry what it takes to largely supply their escort ships when necessary.
Not that I have any personal experience in this area.
Maybe others here can speak to that.
I remember we would sometimes refuel smaller ships like a destroyer in our group. The carrier can give lot's of other support in anything from Post Office to Machine Shop, Motor Rewind Shop, small engine shop, O2N2, supplies, full surgical and dental care, pharmacy, and lots more.