refactor: load agent identity runtime eagerly (#19763)

## Summary

AgentIdentity auth previously registered the process task lazily behind
a `OnceCell`. That meant the auth object could be constructed before its
runtime task binding was known.

This PR makes AgentIdentity auth load the runtime task at auth load time
and stores the resulting process task id directly on the auth object.
The model-provider call path can then read a concrete task id instead of
handling a missing lazy value.

## Stack

1. [refactor: make auth loading
async](https://github.com/openai/codex/pull/19762) (merged)
2. **This PR:** [refactor: load AgentIdentity runtime
eagerly](https://github.com/openai/codex/pull/19763)
3. [fix: configure AgentIdentity AuthAPI base
URL](https://github.com/openai/codex/pull/19904)
4. [feat: verify AgentIdentity JWTs with
JWKS](https://github.com/openai/codex/pull/19764)

## Important call sites

| Area | Change |
| --- | --- |
| `AgentIdentityAuth::load` | Registers the process task during auth
loading and stores `process_task_id`. |
| `CodexAuth::from_agent_identity_jwt` | Awaits AgentIdentity auth
loading. |
| model-provider auth | Reads a concrete `process_task_id` instead of an
optional lazy value. |
| AgentIdentity auth tests | Mock task registration now covers eager
runtime allocation. |

## Design decisions

AgentIdentity auth now treats task registration as part of constructing
a usable auth object. That matches how callers use the value: once auth
is present, the model-provider path expects the task-scoped assertion
data to be ready.

## Testing

Tests: targeted Rust auth test compilation, formatter, scoped Clippy
fix, and Bazel lock check.

codex-rs/models-manager/src/manager_tests.rs

@@ -9,9 +9,6 @@ use codex_login::ExternalAuth;
 use codex_login::ExternalAuthRefreshContext;
 use codex_login::ExternalAuthTokens;
 use codex_login::TokenData;
-use codex_login::auth::AgentIdentityAuth;
-use codex_login::auth::AgentIdentityAuthRecord;
-use codex_protocol::account::PlanType;
 use codex_protocol::openai_models::ModelsResponse;
 use pretty_assertions::assert_eq;
 use serde_json::json;
@@ -237,18 +234,6 @@ c2ln",
         .expect("auth should be present")
 }
 
-fn agent_identity_auth_for_tests() -> CodexAuth {
-    CodexAuth::AgentIdentity(AgentIdentityAuth::new(AgentIdentityAuthRecord {
-        agent_runtime_id: "agent-runtime-id".to_string(),
-        agent_private_key: "agent-private-key".to_string(),
-        account_id: "account-id".to_string(),
-        chatgpt_user_id: "chatgpt-user-id".to_string(),
-        email: "agent@example.com".to_string(),
-        plan_type: PlanType::Pro,
-        chatgpt_account_is_fedramp: false,
-    }))
-}
-
 #[tokio::test]
 async fn get_model_info_tracks_fallback_usage() {
     let codex_home = tempdir().expect("temp dir");
@@ -713,43 +698,6 @@ async fn refresh_available_models_fetches_with_chatgpt_auth_tokens() {
     );
 }
 
-#[tokio::test]
-async fn refresh_available_models_fetches_with_agent_identity() {
-    let dynamic_slug = "dynamic-model-only-for-test-agent-identity";
-    let codex_home = tempdir().expect("temp dir");
-    let endpoint = TestModelsEndpoint::new(vec![vec![remote_model(
-        dynamic_slug,
-        "Agent Identity",
-        /*priority*/ 1,
-    )]]);
-    let manager = openai_manager_for_tests_with_auth(
-        codex_home.path().to_path_buf(),
-        endpoint.clone(),
-        Some(AuthManager::from_auth_for_testing(
-            agent_identity_auth_for_tests(),
-        )),
-    );
-
-    manager
-        .refresh_available_models(RefreshStrategy::Online)
-        .await
-        .expect("refresh should fetch with agent identity");
-
-    assert!(
-        manager
-            .get_remote_models()
-            .await
-            .iter()
-            .any(|candidate| candidate.slug == dynamic_slug),
-        "remote refresh should include models fetched with agent identity"
-    );
-    assert_eq!(
-        endpoint.fetch_count(),
-        1,
-        "endpoint should fetch models with agent identity"
-    );
-}
-
 #[test]
 fn build_available_models_picks_default_after_hiding_hidden_models() {
     let manager = static_manager_for_tests(ModelsResponse { models: Vec::new() });
@@ -768,35 +716,6 @@ fn build_available_models_picks_default_after_hiding_hidden_models() {
     assert_eq!(available, vec![expected_hidden, expected_visible]);
 }
 
-#[tokio::test]
-async fn static_manager_treats_agent_identity_as_backend_auth_for_filtering() {
-    let chatgpt_only_model = {
-        let mut model = remote_model("chatgpt-only", "ChatGPT Only", /*priority*/ 0);
-        model.supported_in_api = false;
-        model
-    };
-    let api_model = remote_model("api-model", "API Model", /*priority*/ 1);
-    let manager = StaticModelsManager::new(
-        Some(AuthManager::from_auth_for_testing(
-            agent_identity_auth_for_tests(),
-        )),
-        ModelsResponse {
-            models: vec![chatgpt_only_model, api_model],
-        },
-        CollaborationModesConfig::default(),
-    );
-
-    let agent_identity_models = manager.list_models(RefreshStrategy::Online).await;
-
-    assert_eq!(
-        agent_identity_models
-            .iter()
-            .map(|model| model.model.as_str())
-            .collect::<Vec<_>>(),
-        vec!["chatgpt-only", "api-model"]
-    );
-}
-
 #[tokio::test]
 async fn static_manager_reads_latest_auth_mode() {
     let auth_manager =