Using OTEL_EXPORTER_OTLP_METRICS_HEADERS with prometheusremotewrite

Question

My use case is that I would like to setup a opentelemetry-collector gateway in a multi-tenant type format. So instead of hardcoding the prometheusremotewrite Authentication header for a single tenant, I was hoping I could use the OTEL_EXPORTER_OTLP_METRICS_HEADERS with each tenant and they would send their credentials as a header. The prometheusremoteagent would then apply this to it's writes to a Cortex backend, storing each tenants metrics into their own tenant space. Is this something that is possible right now?

I have tried setting up an application and otel-collector with the following setups.

# otel-collector-config.yaml
receivers:
  # Data sources: traces, metrics, logs
  otlp:
    protocols:
      grpc:
        endpoint: 0.0.0.0:4317
      http:
        endpoint: 0.0.0.0:4318

processors:
  # Data sources: traces, metrics, logs
  batch:

exporters:
  # Data sources: metrics
  prometheusremotewrite:
    endpoint: "https://<cortex_endpoint>/api/prom"
    external_labels:
      team: foo
      env: bar

service:
  pipelines:
    metrics:
      receivers: [otlp]
      processors: [batch]
      exporters: [prometheusremotewrite]

For my application, I've added the env variable: OTEL_EXPORTER_OTLP_METRICS_HEADERS=Authorization=Bearer "<id>:<token>"

This doesn't seem to be working though, at least I'm not seeing metrics populated in my datasource, but I'm not seeing any authentication errors from the prometheusremotewrite exporter either.