The Sunny Island and Sunny Boy work great together. So long as grid is up, frequency is between 59.4 and 60.4 Hz. Sunny Boy delivers all power available from PV for net metering. If grid goes down, after about 30 milliseconds Sunny Island lifts a relay and produces AC. Almost all appliances, computers etc. ride through, don't notice the dropout. Sunny Boy probably drops off, and Sunny Island powers loads from battery. In a couple minutes, Sunny Boy comes back online and everything runs. If battery is full and loads are less than PV production, Sunny Island increases frequency. Up to 61 Hz, Sunny Boy produces 100% of available power. Linearly up to 62 Hz, Sunny Boy decreases power to 0%. So as I add or remove loads, frequency moves between 61 Hz and 62 Hz, and Sunny Boy adjusts output to match load (air conditioner, fridge, etc.) Sunny Island takes care of starting surge current for motors. At night, things run on batteries. Sunny Island puts out < 59 Hz for a while to mechanical timers average out to correct time.
That all works if inverter is set to respond to frequency shift. Other brand grid tie inverters drop off above 60.5 Hz. A Sunny Boy set for on-grid UL-1741 does the same. The new "grid support" parameters allow some frequency/voltage excursions and may have some power adjustment in response, but not as good. The various model Sunny Boy either need an RS-485 cable and adapter or setting changed to "off-grid" a.k.a. "island". SMA started shipping Sunny Boy already configured with backup mode "on all phases" so just plugging in hardware enabled the function.
My Sunny Boy were SWR2500U, from 15 years ago, and couldn't be set with the necessary parameters. I picked up some 10000TLUS which are listed as compatible. With parameters set and RS-485 connected, they recognized off-grid and stayed connected up to 62 Hz, but didn't reduce power output. SMA support told me to set the for off-grid. That works fine, and no RS-485 needed. They just can't be wired directly to grid, because they don't have UL-1741 enabled, have to be connected through Sunny Island.
Your -41 model don't even have an RS-485 interface. They have an interface like Ethernet which would work with Sunny Boy Storage. I think the new Sunny Island models in Europe may support them. Those are also rain tight, don't have the breaker or SD card. For the US Sunny Island, SMA support told me to just configure -41 for off-grid.
If you can wire additional circuit breaker panels, you can set up a protected loads panel with things like refrigerator, internet, some lights. It would always be connected through Sunny Island, total of about 50A 120V available. With only one Sunny Island you need the transformer, to deliver 25A 240V & 50A 120V. You should also have the "load shed" relay to disconnect loads but leave Sunny Boy connected; otherwise if battery is drained Sunny Island will shut off and never turn back on. You would need a battery charger to recover from that.
To use your generator as well, need a transfer switch so input to Sunny Island is connected to either grid or generator. Use a switch or extra relay contact to tell Sunny Island which. It will let Sunny Boy backfeed the grid but not the generator. It closes a relay to autostart generator, or that could signal you to manually start.
For 11 kWh at night you would need 400 Ah 48V battery, $5000 for AGM like mine. If you could get that down to 3 kWh then $1200 for 100 Ah. Or less money for FLA like golf cart batteries.