For AC coupling, it takes a couple of seconds to shift frequency and curtail production. For Sunny Island, SMA recommends 100Ah of 48V battery per kW of AC coupled GT PV (e.g. Sunny Boy).
I'm using AGM, which can accept a high charge current, and have maybe 30% the recommended size.
It should actually be more an issue of how many kW of "load dump" (load suddenly taken offline), rather than actual load. But since my system exports to grid, dropping grid may count as load dump, or maybe Sunny Boys disconnect due to loss of grid before Sunny Island takes over.
With DC coupled PV such as SolArk, it can curtail production faster.
Lithium batteries will run toward over-voltage when charging occurs, so they need SoC and balancing such that system remains on line.
What charge rate do your batteries accept? 0.5C? You could plan bank sized based on that, or you could program inverter to limit charge current despite an oversize PV array, as I did. PV is able to supply all loads during sunny days plus recharge battery.
If your lithium batteries can get cold, max allowed charge current drops toward/to zero amps as temperature approaches freezing. So 0.5C charge rate would be excessive if batteries were 10 degrees C.
And then it depends on your objective.
For me, it was just enough battery to make it through the night during power failure.
Depending on time of use rate schedules, you might want to store 100% of production to export or offset loads later in the day, so battery capacity about 6kwh for every 1kW of PV.
For extended off-grid operation, traditionally people aimed for 3 days worth of storage.