What we now call LF has an isolation transformer with battery voltage applied to primary, AC voltage on secondary.
I think my Sunny Island is 42V in, 170Vpeak out.
But these actually have HF PWM to synthesize sine wave.
What we call HF inverters just use inductor or HF transformer to create boosted AC voltage. Or, HV battery, just buck or buck-boost to AC voltage with HF inductor or transformer.
A true LF inverter would be MSW, like 12V applied to primary, 170V from secondary. Or multiple transformer taps to make staircase. Like early Trace and Warpverter.
Putting an auto-transformer or an isolation transformer after an HF inverter, inside or out, does not make it LF.
But when the transformer is step-up from 48V battery to 120 or 120/240Vrms, we call it LF. Not sure that is accurate.
Transformer does not do anything to provide high surge. MSW architecture does, limited I think to fault current capability of transformer (many times nominal.)
HF can have surge if transistors and boost inductor can deliver it. Usually limited in time due to heating.