[app-server] Expose custom ThreadStore injection

We run multiple app-server instances and need threads to be stored in a shared backend so they can be accessed consistently across instances. Examples include object storage such as Azure Blob Storage, or another externally managed database or service.

ThreadStore already provides the required abstraction, but app-server constructs it internally and exposes no dependency-injection point for embedding hosts.

Desired API example:

let storage = AppServerStorageDependencies {
    thread_store: Some(Arc::new(CustomThreadStore::new(...))),
    queue_store: None,
};

run_main_with_transport_options_and_storage(..., storage).await?;

Could app-server expose a process-scoped API for supplying a custom ThreadStore and optional QueueStore, while keeping the current local storage behavior as the default?

Prototype: Reference implementation: custom ThreadStore injection

Related: https://github.com/openai/codex/pull/21596

Start by reading the existing ThreadStore abstraction and the app-server entry point run_main_with_transport_options_and_storage, then compare the proposed AppServerStorageDependencies shape with the prototype and related pull request. Done means embedding hosts can supply a custom ThreadStore and optional QueueStore while existing local storage remains the default.