The log seems indeed odd to me.
It seems that somehow the battery channel works, but the dimmer one only appears once.
You should also actually see a log entry even without any rule, just by clicking the button as it should transmit the zigbee signal to the binding (I think, as mentioned, not using the binding).
It also seems the device is not on the bindings documentation list, though some other remotes still worked (?).
I can also only find posts talking about the remote with z2mqtt.
Will keep digging and report if I find anything else.