Why are these changes needed?

See #44226 for more details, but TL;DR:

• The REST API is declarative, meaning if you deploy a config that does not contain some running applications, they will be deleted.
• However, in some cases users mix-and-match this declarative API with the imperative serve.run API. In this case, we should not delete the dynamically-created apps.
• This PR addresses it by tracking the APIType and only deleting apps that were applied via the declarative API. There is no public API change. In the future we may want to consider exposing this metadata so external systems like Kuberay can treat the types of apps differently (e.g., for determining high-level status).

Related issue number

Closes #44226

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• I've included any doc changes needed for https://docs.ray.io/en/master/.
  • I've added any new APIs to the API Reference. For example, if I added a
    method in Tune, I've added it in doc/source/tune/api/ under the
    corresponding .rst file.
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• Testing Strategy
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  • This PR is not tested :(