According to the table, anything larger that 1,100 kcmil requires 3/0 Copper (or 250 kcmil Aluminum). Since you're running parallel sets, you need to run that size ground wire with each set.
I read the chart to say 3/0 is the biggest conductor you ever need and I agree the grounding conductor does not need to be run in each set. They are not usually even going to the same place.
The water ground is max 3/0 Cu by NEC, however the design professional may spec something larger. Terminations are at the street side of the water main, and on a compliant sized lug within the main OCP enclosure on the neutral buss.
This conductor does not go with the feeder conductors, as others have said