Did you enable the MQTT integration?
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Sorry for my stupid question... where?
I have Mosquitto broker and Zigbee2MQTT. I watched many videos on YT, but none could give me hints what to do.
Setting - devices and services - add integration - MQTT
Zigbee2MQTT only takes care of the devices themselves. The HA MQTT integration pulls those devices in so you can use them in HA. Should look like this

OK, I'll try to add my plugs via add device.
Should not be necessary. Define your Zigbee2mqtt server and it should pick them up automatically.
I tried and gloriously failed. I will rtfm this week and maybe your answers make sense. All the Videos on YT show a different GUI.
Post screenshots of what you're seeing on your system.
Wahrscheinlich reden wir aneinander vorbei.
Dauert aber bis zum Wochenende. Ich bin nur Freitag bis Sonntag in der Hütte in der ich mich in HA einarbeite.