I'll throw this out there even though it's not directly related, as I'm using the Jackery system, but it is my opinion that you don't have to worry about it because you're not feeding the main panel any additional input. The Jackery panel also comes with a 100 amp breaker, and is integrated into a 12-slot transfer switch. I assume you will be working with a transfer switch as well, yes?
So here's the thing: if you're dumping raw solar input into your home panel, then yes the 120% rule applies. But in these cases we're not. Because you're not dumping raw power in. You're instead removing capacity out of your main panel, and transferring it to the sub panel/transfer switch, and the transfer switch can either power the circuits through grid power or through power station power, but not both. You won't be powering anything new, or putting more power into the panel at all.
Check
this doc, I hope it explains what I'm surely failing to.
AIUI, the worry in the NEC is that when you add a second power source to the main panel (external solar input), then you're increasing how much power is flowing through not only the breakers but also the busbars, and can therefore overload the bus bar or other connections or wiring, etc. That main breaker was sized to that panel and that wiring as a complete system, so arbitrarily dumping another huge load of power into it can cause a fire.
But we're doing the opposite. In the Jackery's case, we're actually moving all three wires from the circuit breaker off the main panel, over to the transfer switch, and the transfer switch handles whether it's going to use grid or power station input to feed that circuit. Which means there's zero additional power flowing through the main panel; in fact there's usually going to be LESS power flowing through the main panel! Any solar input to the power station cannot be backfed into the main panel, it can only be fed through the subpanel/transfer switch. And any circuits that the solar/battery system powers, will be circuits that are not drawing on the main panel, so the net effect will be that the main panel is handling less energy in most conditions than it currently is. The 120% rule doesn't apply at all in these conditions because we haven't added any input to the main panel at all.
I would imagine the F3800 system behaves similarly, in that it can't backfeed into the main panel and because it uses a transfer switch, the net effect should be no additional power on the main panel, which would (AIUI) negate any need to invoke the 120% rule.
Hopefully a qualified electrician will be along soon to clarify any mistakes in what I've written.