I finally got this to work. Unlike what the description here says, this is how to update the value:
In Home Assistant, go to Developer->Service->YAML mode:

service: text.set_value
data:
  value: "967067"
target:
  entity_id: text.water_meter_100_2

(change 967067 with the value you want to add to the current counter)

The service "notify.mysensors" seems to be deprecated by Home Assistant.

I really like the update you did for Home Assistant integration.

But: I do not really understand, how to correctly send the VALUE_TO_ADD.

This is what I tried to add 967.067 m³:

service: notify.mysensors
data:
  message: VALUE_TO_ADD
  target: text.water_meter_100_2
  data: 967067

But I just get this error message:

Fehler beim Aufrufen des Diensts notify.mysensors. expected dict for dictionary value @ data['data']. Got None

These are my newly found entities:

What is wrong here?