How can I make Prometheus metrics collected by AWS Cloudwatch appear as metrics in Cloudwatch?

I have a Java service running in Fargate which exports Prometheus metrics via an /actuator/prometheus endpoint. It is my understanding that the only way to get Prometheus metrics into Cloudwatch is to deploy a Cloudwatch Agent in the Fargate cluster, and have the agent collect the metrics.

After much struggle, I have managed to get the Cloudwatch Agent deployed to the cluster. It also seems to collect metrics exported by the service.

However, the metrics ends up in a log group named /aws/ecs/containerinsights/{name}/prometheus. An example of a single log line can be found below.

How do I get those metrics into the "metrics" section of Cloudwatch? Right now, it seems that the metrics only makes it into a log, which provides no real value. I'd like to be able to browse and graph the metrics. I am unable to find these metrics in the Container Insights or the metrics section.

{
    "ClusterName": "[...]",
    "ECS_PROMETHEUS_NAME": "[...]",
    "ECS_PROMETHEUS_PATH": "/actuator/prometheus",
    "ECS_PROMETHEUS_PORT": "9082",
    "LaunchType": "FARGATE",
    "StartedBy": "ecs-svc/8880037603679832257",
    "TaskClusterName": "[...]",
    "TaskDefinitionFamily": "[...]",
    "TaskGroup": "service:[...]",
    "TaskId": "a57784efbb124bcfa4d3291cc51f4694",
    "TaskRevision": "442",
    "Timestamp": "1697115231324",
    "Version": "0",
    "area": "heap",
    "container_name": "[...]",
    "id": "G1 Eden Space",
    "instance": "10.1.177.38:9082",
    "job": "[...]",
    "jvm_memory_committed_bytes": 170917888,
    "jvm_memory_max_bytes": -1,
    "jvm_memory_used_bytes": 11534336,
    "prom_metric_type": "gauge"
}