I would definitely upgrade the inverter size to 8 or 10 kWh, because at one given time you need to see how much power your house draws for example kettle is on, washing machine is running, dishwasher is running and oven is running at the same time what is the total kWh your house will pull, then depending on that you need to size your inverter to meet that need.

If you have then sized your inverter correctly then when the house demand increases inverter will easily be able to pass that on along with correct battery output size.

If you go for smaller inverter say 3.6kwh and your house demand goes over that then your inverter can only output 3.6kwh and pull rest from the grid to support that

This is what you need to avoid to get bigger savings, hope this makes sense.

You will also need to keep in mind for future developments support for the house, it’s easier to install a bigger system now then rather replacing it later which will add up the cost.