I have a 3 phase setup configured with 3 5kW deye inverters (which are very similar to the sunsynk inverters). When one phase is overloaded (running dryer+AC, for example), the inverter connected to that phase shuts down with an overload error and the other two also shut down with a communication error. All power to the loads is lost for a short time until the inverters restart.
If grid power drops a phase this will probably be interpreted as a total grid failure and all inverters will probably switch to PV+battery but it's not possible for me to test this.