[ML] Refactor stream metrics

[prwhelan]

Remove the use of DelegatingProcessor and replace it with an inline processor.

---

Verified that metrics still publish:

{
  "_index": ".ds-metrics-apm.app.elasticsearch-default-2025.03.11-000001",
    "@timestamp": "2025-03-18T12:42:56.587Z",
    "numeric_labels": {
      "status_code": 200
    },
    "service": {
      "node": {
        "name": "runTask-0"
      },
      "version": "9.1.0"
    },
    "host": {
      "hostname": "whelan-elastic",
      "os": {
        "platform": "Linux"
      },
    },
    "metricset": {
      "name": "app"
    },
    "es.inference.requests.time": {
      "counts": [
        2
      ],
      "values": [
        9888.5
      ]
    },
    "labels": {
      "otel_instrumentation_scope_name": "elasticsearch",
      "service": "cohere",
      "rerouted": "false",
      "model_id": "command-r-plus-08-2024",
      "task_type": "completion",
    },
  },
}

[elasticsearchmachine]

Pinging @elastic/ml-core (Team:ML)

[prwhelan]

Publisher has a single method subscribe, so when our downstream calls subscribe we will forward it to the upstream.subscribe, tying the upstream and downstream together with this function

[elasticsearchmachine]

💔 Backport failed

Status	Branch	Result
❌	8.x	Commit could not be cherrypicked due to conflicts

You can use sqren/backport to manually backport by running backport --upstream elastic/elasticsearch --pr 125092