I had a very similar system to yours installed in April last year. GE 3.6kW Hybrid inverter, 10 x 415w panels on a ESE roof & 9.5kWh Gen 2 battery. Zappi & Eddi also installed at the same time. No HP (yet) so I'm still on gas for heating & HW.
After the install all went well & I managed to self consume up to 90% of all my generation until the winter months arrived when, depending on usage & without much solar top up, the 9.5kWh battery kept running out from 12noon onwards (we are at home most days). Also, I was constantly second guessing the next day's weather in order to maximise solar battery & EV charging during the day to avoid having to pay to unnecessarily overcharge the battery at night or use grid power during the day (I was a std variable rates & I had no export tariff at that time).
I therefore decided to add an extra 9.5kW battery & an extra 5 x 425wp panels on a NW roof to catch mid afternoon & evening generation & these got installed earlier this year. The 2 x 9.5kWh batteries now last throughout the day until the cheap rate tariff kicks in which is great.
After Octopus approved our EV & charger combo I switched to Intelligent Octopus Go earlier this year & got an export tariff so now my charging routine is different.
Irrespective of the next days weather I now charge the batteries to their max every night between 11.30pm & 5.30am @7.5p/kWh which means any excess generation the next day goes straight back to the grid & earns 15p/kWh. This is great for the summer months & I am starting earn some decent export income (on sunny days) to offset the overall energy bills. However, with double the battery storage installed, it now takes longer & costs more to get the batts charged up & keep them at 100% to force any excess back to the grid & get paid for it.
I guess it's a "6 to 1 half dozen the other" scenario. The extra battery capacity helps massively during the winter months but could be construed as a hinderance during the summer. I think this is why some Octopus users switch tariffs from winter to summer. Personally I'm not sure that makes any sense for us but I'm willing to be persuaded otherwise.
Time will tell after a full year of use how much extra I have manage to save by adding another battery & extra panels. However, this year I have already claimed back £1,500 from my Octopus account because I was over £1,800 in credit (I didn't reduce my DD payments after the solar was installed). I have also now reduced by DD monthly Octopus payments by over half so for me the whole solar thing is starting to work.
As ever though, & like many others on this forum, I'm still tweaking how I use & control the system to suit what we need & achieve the best results.
Based on my experience the extra battery was worth it but getting the right size will depend on your daily usage & any future plans you have e.g. adding a HP to replace a gas boiler. Battery prices have dropped quite a bit & there's no VAT now so going larger is not so much of an issue now than it was a 6 months ago.
I hope this helps.