[ECR] Make prefix optional on pull through caches

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**Tell us about your request**
When configuring an ECR pull through cache for `public.ecr.aws`, we're forced to set a namespace prefix. For example `public.ecr.aws/datadog/agent:7.46.0` might gain an `ecr-public` prefix and become `.dkr.ecr.us-east-1.amazonaws.com/ecr-public/datadog/agent:7.46.0`.

This is a hassle because a number of tools in the docker ecosystem (like buildkit) support auto mapping of registry hosts (like `public.ecr.aws` to `.dkr.ecr.us-east-1.amazonaws.com`), but they don't support automatically adding a prefix to the image reference.

As a result, we must change our `Dockerfile`s and `docker-compose.yml`s to use the pull through cache images explicitly. It would be super nice if we could leave them referencing `public.ecr.aws/datadog/agent:7.46.0` and the mapping could happen under the hood. This would be possible if the `ecr-public` prefix was made optional.

This would be particularly helpful because it would leave the `Dockerfile` and `docker-compose.yml` in a shape that works for unauthenticated users on local machines.

**Which service(s) is this request for?**
ECR

**Are you currently working around this issue?**
We are changing `Dockerfile` and `docker-compose.yml`to use the private ECR reference, but it requires users to login locally, and it prevents tools like dependabot from being able to update the files (they don't have access to our private ECR).

Review the ECR pull-through cache request and the Dockerfile and docker-compose.yml workaround described in the issue. The desired outcome is for public.ecr.aws image references to work without adding a namespace prefix, while preserving unauthenticated local use and allowing tools such as Dependabot to update the files; no implementation files or tests are named.

Written by the indexing model from the issue text.