When you run your system closed loop (in Lithium mode) the voltage setting in the inverter that regulate charging gets ignored and the BMS take precedence.
The maximum charge amps and discharge amps set in the inveter will remain and the inverter will not charge or discharge more than this setting even if the BMS allows for more. This is only true if the charge /discharge setting in the inverter is lower compared what the BMS allows, if the inverter setting is higher the BMS setting takes precedence.
There has been a few post that states that in lithium mode the BMS reports average SOC to the inverter. This is not always true. Pylon does average, PACE and a few others reports lowest SOC during discharge and highest SOC during charge. Most cheaper BMS just follow what Pylon does and reports average.
The BMS will have a low SOC warning setting, generally this is the SOC level, when using closed loop, at which point the BMS will force the inverter back to grid.
When using open loop (AGM mode) the low warning SOC level is just a warning. The SOC indicator lights, or one of then, generally starts flashing red at this point, but it does not stop battery discharging. The battery will only stop discharging once the cell or pack UVP is reached (so it is voltage based in AGM mode and SOC based in lithium mode).
In AGM mode, even when the batteries are connected to each other with the link cables, one battery shutting down due to reaching the UVP voltage level will not impact any others which can continue to discharge.
Tehcnically this cannot happen in Lithium mode due to the low SOC cut off unless there are large SOC differences between batteries.
@Hanno Labuschagne The 56.5v charge voltage in the picture is low. What is the maximum charge voltage per the battery manual?. Perhaps set this setting in the inverter and charge using AGM mode and see if this resets the SOC counter and if they are then closer to each other during discharge.
Quick google for the manual states work voltage up to 57.6v (or 3.6v per cell). Manufacturers often change this setting as they develop their product, it might be that your two batteries have different setting especially if one is version 1 and the other version 2.