Prometheus and Prometheus operator already support custom Authorization for remote write. This should be possible to configure the same in the CMO configuration:

apiVersion: v1
kind: ConfigMap
metadata:
  name: cluster-monitoring-config
  namespace: openshift-monitoring
data:
  config.yaml: |
    prometheusK8s:
      remoteWrite:
      - url: "https://remote-write.endpoint"
        Authorization:
          type: Bearer
          credentials:
            name: credentials
            key: token

DoD:

• Ability to configure custom Authorization for remote write in the openshift-monitoring/cluster-monitoring-config configmap
• Ability to configure custom Authorization for remote write in the openshift-user-workload-monitoring/user-workload-monitoring-config configmap