It is true that if your generator or other power generating system (ie: Bluetti battery stations) functions as a separately derived system, in other words it has its own ground/neutral bonding system, then the transfer switch needs to also switch the ground and neutral wiring between sources.
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If, however, the generator or other power generating system does not have it’s own ground/neutral bonding, in other words it has a floating ground, then it needs to connect to the existing (ie: main panel) ground and neutral and does not need the transfer switch to also switch the ground or neutral conductors.
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The reason for this is because there cannot be multiple neutral to ground bonding sites.