How to add labels in standalone Elastic Agent synthetics input configuration

I want to add labels to a standalone elastic agent input configuration. This works with a regular system/metrics input, but doesn't seem to work for a synthetics/monitor configuration.

Already read about some differences for synthetics, where it seems you need to use "add_fields" instead of "add_labels". But still no luck with this yet.

Example config using "add_fields":

inputs:
  - type: synthetics/http
    id: app/synthetics-http
    use_output: synthetics
    data_stream.namespace: default
    processors:
      add_fields:
        target: labels
        fields:
          customer: X
    streams:
      - type: http
        name: app-http
        data_stream:
          dataset: http
          type: synthetics
        hosts: []
        schedule: '@every 30s'
        timeout: 5s

Like this

inputs:
  - type: synthetics/http
    id: app/synthetics-http
    use_output: synthetics
    data_stream.namespace: default
    streams:
      - type: http
        name: app-http
        data_stream:
          dataset: http
          type: synthetics
        hosts: []
        schedule: '@every 30s'
        timeout: 5s
        fields:
          labels:
            customer: x