geoffreycoan I can confirm that a chain of 5.2kWh batteries are in parallel not series and will charge at the full 3kW on my inverter even though each battery is limited to 2.6kW so both a 3.6kW inverter and a 5kW inverter will be able to work at their limits charging 2 or more batteries. The current is shared between the batteries.
Having a primary and secondary battery with the chain passing through the primary to get to the secondary doesn't put them in series electrically. They are both joined to the same plus and minus cables. You can verify this by measuring the resistance (with the batteries and inverter shut down) between the positive in connector and positive out connector in the primary battery. I think it has been done this way to avoid the primary having to switch or control high currents to the secondary (through a relay or FETs) and it also means a single battery fault (or it being switched off) doesn't bring the whole chain down.
One benefit for me of the inverter having a limit of 3kW is that each of my batteries only ever charges and exports at 1.5kW and are thus treated a little more gently over their lifetime. My son has a single 9.5kWh battery on his system and is therefore limited to the battery limit of 2.6kW and is always charging and exporting at this limit unless he chooses to drop the current in the app (which he doesn't). This is treating the battery more harshly although whether it really makes much difference over the battery life is yet to be seen.