A 2-pole 50A breaker on 120/240V split-phase service, at 80% continuous load, is sufficient for 9.6kW
A Sunny Island can pass up to 56A in either direction through its relay connecting AC1 and AC2.
A 70A thermal-magnetic breaker seems appropriate, with 6 awg or 4 awg wire (hot location 4 awg for 70A, although we never expect that much current.)
For some reason manual says max 56A breaker on AC1.
I'm now using 60A Midnight/CBI magnetic/hydraulic breaker, guaranteed no-trip below 63A. Also have Carlingtech 70A guaranteed no-trip below 70A.
If you connect SI AC2 to grid, battery will charge whenever grid is up. After a glitch following power failure it will supply AC1 from battery.
If you want PV to keep SI and its battery operating during an extended power failure, yes you want Sunny Boys on AC1 island side.
If you have 2x SI in a 120/240V system, 56A current limit means 13.4kW maximum PV for grid-tied. (Off-grid, up to twice SI rating so about 24kW).
If you had two SB 7.7, with enough PV to possibly exceed 13.4kW, I would suggest putting one behind SI and keeping other on main panel. Use manual interlocked breakers to feed main panel from SI during extended grid outage.
If using SB with SI, it should be set to UL-1741-SA (Rule-21), or "backup" with RS-485 interface for older models. "off-grid" works great, but is not correct and safe according to documentation (SI appears to provide utility worker protection because it performs anti-islanding and can isolate from grid, but relays can weld closed.)
Diagram:
An interlocked breaker panel for "load" is useful to bypass SI if it fails.
A load-shed relay is useful to disconnect excessive loads so SI keeps operating until sun comes up and SB can again produce.