That is not how it works when PV is available.
The MPPTs make the panel voltages into the desired voltage for the AC inverter (usually about 350 volts DC which is optimum for making 240 VAC and why making strings that produce about 360 volts DC is best for MPPT efficiency). There is no going through the battery for PV to AC.
The battery charger works from the MPPT output voltage. The battery discharge runs through a booster to make the 360 volts DC for the inverter. The battery path is not involved in the PV to AC direct path. In this way, the string inverter is really just a big microinverter, same energy conversion process, but with a battery charger and booster to the side.
This is one reason why inverters with high voltage batteries are more efficient, the battery buck and boost conversions are more efficient than doing it at 48 volts, and cheaper since current is what drives cost for the most part.
This design is also why an inverter can have 12 KW AC output (the size of the AC inverter) but take in 18 KW of PV (like the EG4 18KPV). 6 KW is being used by the battery charger separately from the AC power path.
Basically, the AIO hybrid is NOT a battery charger followed by a battery inverter. There is a direct path of PV to AC.
When there is no sun, then the system has to charge the battery during the day and then use the battery during the night. But this is done with more efficient DC conversions than doing AC twice like a microinverter.
Mike C.