Relay disconnect of output (or input) when autotransformer disconnected should work. So long as it is just a transformer, without an over-temperature thermostat (don't think it has one.)
Is it the .pdf schematic in OP's post #1 you're referring to? I think others were posted somewhere in these 42 pages.
A simpler solution, but only supporting 120V total current up to transformer's capability not current imbalance to its capability, would be connect inverters to a 240V only loads panel, then use 25A dual breaker to feed autotransformer and 120V loads panel (no separate breaker for transformer, just tapped off main lugs). If breaker trips, autotransformer and 120V loads are disconnected.
However you do it, use wire gauge capable of carrying 50A for auto-transformer neutral. That's how much current will be in neutral if L1/L2 are each carrying 25A. Data sheet lists 42A (48A for 208V input) line to neutral current.
The data sheet I've found for one GroWatt transformer model appears to implement relay disconnect for lost neutral as you propose (different from what's in post #1), but details of internal wiring aren't sufficient to be sure:
"The rated power of secondary side L1-N and L2-N could up to 5kVA respectively, and the power difference between the two split phases can not exceed 1.5kW."
???
1.5kW / 120V = 12.5A
Are they saying that a single 120V, 1500W, 12.5A load on one phase and zero on the second phase is maximum it can handle?
Of course balanced loads, either 240V only load or identical sized 120V loads on two phases wouldn't involve the transformer.
But if 1.5kW is the most imbalance either 5000VA rated ATS 5000T-US or 11400VA rated ATS 11400T-US can handle, that is only 750VA actually going through the transformer core.
I suspect that someone who misunderstands transformers wrote that line, while the specs for amps per wire are correct.
Note that these two models, with quite different max power rating, have identical "Max continued current(L-N)".
That means they are the same transformer, but have different contactor. Victron similarly offers theirs with two different L1/L2 ratings but same autotransformer.