It doesn't matter if HF or LF inverters but they need to have serial capability.
Not only is sync (180 degs out of phase lock) necessary, but also coordinated operation, like if one inverter shuts down for any reason, the other also shuts down. There are other coordination's for other features, like charging.
Calibration is critical. If one inverter float and/or absorb charging settings is off calibration the two inverters can fight each other on the same battery.
Two series inverters have an advantage on AC input neutral imbalance as the two inverters can independently match their respective L-N grid voltage. On LF inverters when one side of AC L-N has a glitch it will create a momentary 'swapping of current' between the two inverters via common battery connection as the inverter(s) adjust to their glitched or varied L-N voltage.
One tricky part is when AC input goes open circuit, like if you flip off AC input breaker. Zero AC input current is a legitimate condition that does not cause pass-through relay to disconnect. Unless inverter has an active UL1741 phase wobble test, the inverter may not realize the AC input has gone open if AC input current is low.
When this happens, the inverter will wander off in frequency since, when pass-through relay is engaged, the inverters track to their respective L-N AC input phase and frequency. Inverter will eventually wander outside of freq range limits causing pass-through to release, but this wreaks havoc on 240 vac output due to freq wander.
It is not until pass-through relay is released that the inverter also switches to its own frequency reference and then relies on sync with other series connected inverter.
Inverter phase sync has to make a hard decision when to sync to AC input or to other inverter. It must be one or the other, and it coincides with pass-through relay engagement. A safety check is inverters monitor phase difference between the two inverters and if it gets too deviant, it decides something must be wrong with AC input and triggers a simultaneous pass-through disconnect of both inverters, slewing back to master inverter's freq/phase reference. Most inverters have an 'early/late' zero crossing phase detector. If it does not get some pulses from the early/late phase detector in a few cycles it usually means something is not right with AC input.