Inspired by the posts above (which did not work for me) - this is my solution:
mqtt:
sensor:
- name: WaterMeter rate per digitalization round L
unique_id: WaterMeter_rate_per_digitalization_round_L
state_topic: "watermeter/main/rate_per_digitalization_round"
value_template: "{{ (value_json * 1000) }}"
unit_of_measurement: L
icon: mdi:arrow-expand-vertical