MQTT Statestream Switch setup advice needed

Configuration
1

I use MQTT statestream communication to exchange states between two Home Assistant instances. This worked fine with sensors. But I failed with a switch, initially set up by the Community Add-on “AdGuard Home”. I’m able to read the switch state from the MQTT broker, but fail to set the switch to a a new state. My initial guesses like “set”, “ON”, etc. dont work. My code snipplets:

mqtt_statestream:
  base_topic: rp42
  include:
    entities:
      - switch.adguard_protection

(Switch)
  - platform: mqtt 
    name: "adguard_protection_137" 
    state_topic: "rp42/switch/adguard_protection/state" 
    command_topic: "rp42/switch/adguard_protection/set" 
    payload_on: "on" 
    payload_off: "off" 
    state_on: "on"
    state_off: "off"
    optimistic: false
    retain: true

mqtt

A clumsy workaround with an additional input_boolean (coupling with a template switch and automations) is working, but painfull to look at.

Suggesions to find a solution, in particular finding the right command_topic string, are appreciated.