Note 2 to 2023 NEC Table 250.66 says "If there are no service-entrance conductors, the grounding electrode conductor size shall be determined by the equivalent size of the largest service-entrance conductor required for the load to be served."
So if there are no SECs, you need to do a load calculation. The load will come out to some number not more than 350A, assuming the two breakers are sized properly. Then size the GEC per the 75C column of Table 310.16 and Table 250.66. E.g. 151-200A = 2/0 or 3/0 Cu = #4 Cu GEC. 201-310A = 4/0-350 MCM = #2 Cu GEC. 311-350A = 400-500 MCM = 1/0 Cu GEC.
Since the GEC is running to the water meter, none of the smaller sizes allowed by 250.66(A), (B), and (C) apply.
Cheers, Wayne
P.S. FWIW Note 2 is actually a bit ambiguous, due to the possibility of parallel conductors. For example, if the load calc came out to 350A, you could use two parallel 2/0 Cu (each of area 133.1 MCM, or 266.2 MCM total) or a single 500 MCM. Those correspond to different sizes in Table 250.66, so you'd use #2 Cu for 2 sets of 2/0 Cu, and #1/0 Cu for a single 500 MCM. Meaning arguably if the load calc is 350A and there are no SECs, you could go for #2 Cu instead of #1/0 Cu. For simplicity I assumed one conductor in the response above.