Pakey07
If you have one inverter for the solar and the battery, you will have a hybrid inverter.
If you have two inverters you will have an AC coupled battery.
If the battery was installed with or after the ASHP, I’d be a bit disappointed you didn’t get suggested the 13.5kWh All In One (AIO) as it has more capacity and a higher discharge rate (5-6kW vs 3.6 for the hybrid vs 3 for an AC).
Also as the AIO is ac coupled also, you max power would have been 5-6kW from battery and 5kW solar (assuming you have a 5kW solar inverter). The hybrid will give a total of 5kW at any time and a max of 3.6kW can come from the battery, but solar+battery will never be >5kW.
Do you have a cheap rate tariff like cosy octopus (referral code available if you don’t have a local friend), which gives you a number of hours at a cheap rate? This would allow you to charge the battery and do most of the ASHP work during the cheap slots, then keep things ticking over between and on solar.