feat: use run agent task auth for inference (#19051)

## Stack

This is PR 3 of the simplified HAI single-run-task stack:

- [#19047](https://github.com/openai/codex/pull/19047) Agent Identity
assertion and task-registration primitives, including the shared
run-task helper used by existing Agent Identity JWT auth.
- [#19049](https://github.com/openai/codex/pull/19049)
Disabled-by-default ChatGPT auth opt-in that provisions/reuses persisted
Agent Identity runtime auth and its single run task.
- [#19051](https://github.com/openai/codex/pull/19051) Run-scoped
provider auth that uses one backend-owned task id for first-party
inference and compaction requests.

[#19054](https://github.com/openai/codex/pull/19054) collapsed out of
the active stack because the simplified design no longer needs a
separate background/control-plane task helper.

## Summary

This PR moves Agent Identity usage into provider auth resolution. That
keeps `AgentAssertion` auth tied to first-party OpenAI provider requests
instead of applying a late session-wide override that could affect
local, custom, Bedrock, API-key, or external-bearer providers.

What changed:

- adds a small `ProviderAuthScope` struct carrying the run auth policy
and session source needed by provider-scoped auth resolution
- lets `Session` opt the existing `ModelClient` into `ChatGptAuth`
policy when `use_agent_identity` is enabled, without adding a second
model-client constructor
- resolves Agent Identity only for first-party OpenAI provider auth
paths
- uses the persisted run task id from the `AgentIdentityAuth` record to
build `AgentAssertion` auth for Responses requests
- routes shared request setup through scoped provider auth so unary
compact requests use the same run-task assertion path as inference turns
- keeps local/custom/Bedrock/env-key/external-bearer provider auth
unchanged
- lets missing run-task state surface through the existing model-request
error path instead of silently falling back to bearer auth

This PR intentionally does not create thread-scoped, target-scoped, or
background-scoped task identities. The run task is the only task Codex
registers in this POC shape.

## Testing

- `just test -p codex-model-provider`
- `just test -p codex-core client::tests::provider_auth_scope_uses`
- `just test -p codex-core remote_compact_uses_agent_identity_assertion`

codex-rs/codex-api/src/auth.rs

@@ -67,6 +67,12 @@ pub type AuthProviderFuture<'a> =
 /// Shared auth handle passed through API clients.
 pub type SharedAuthProvider = Arc<dyn AuthProvider>;
 
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub struct AgentIdentityTelemetry {
+    pub agent_id: String,
+    pub task_id: String,
+}
+
 #[derive(Clone, Copy, Debug, Default, PartialEq, Eq)]
 pub struct AuthHeaderTelemetry {
     pub attached: bool,

codex-rs/codex-api/src/lib.rs

@@ -19,6 +19,7 @@ pub use codex_client::ReqwestTransport;
 pub use codex_client::TransportError;
 
 pub use crate::api_bridge::map_api_error;
+pub use crate::auth::AgentIdentityTelemetry;
 pub use crate::auth::AuthError;
 pub use crate::auth::AuthHeaderTelemetry;
 pub use crate::auth::AuthProvider;