AC Out active in charger mode

That’s how it works. “Charger-only” never switched off the output and it isn’t even possible from hardware design.
Just take a look at the block diagram:


As soon as the relays at the input are closed the AC IN and AC OUT are connected together.
There isn’t an extra charger inside, it uses the same electronics for charging and inverting.

second thoughs
The charger can only be supplied from the AC Bus supplies on either side of the inverter. ( input or output )

Control state of the inverter or charger will not effect the AC supply state. Meaning that the AC output must be live whenever The charger is working.

Inverter and charger states are switched but their outputs go in different directions

sorry for my brain fad