fix: fully revert agent identity runtime wiring (#18757)

## Summary

This PR fully reverts the previously merged Agent Identity runtime
integration from the old stack:
https://github.com/openai/codex/pull/17387/changes

It removes the Codex-side task lifecycle wiring, rollout/session
persistence, feature flag plumbing, lazy `auth.json` mutation,
background task auth paths, and request callsite changes introduced by
that stack.

This leaves the repo in a clean pre-AgentIdentity integration state so
the follow-up PRs can reintroduce the pieces in smaller reviewable
layers.

## Stack

1. This PR: full revert
2. https://github.com/openai/codex/pull/18871: move Agent Identity
business logic into a crate
3. https://github.com/openai/codex/pull/18785: add explicit
AgentIdentity auth mode and startup task allocation
4. https://github.com/openai/codex/pull/18811: migrate auth callsites
through AuthProvider

## Testing

Tests: targeted Rust checks, cargo-shear, Bazel lock check, and CI.

codex-rs/cloud-tasks/src/lib.rs

@@ -68,45 +68,43 @@ async fn init_backend(user_agent_suffix: &str) -> anyhow::Result<BackendContext>
     };
     append_error_log(format!("startup: base_url={base_url} path_style={style}"));
 
-    let Some(auth_manager) = util::load_auth_manager(Some(base_url.clone())).await else {
-        eprintln!(
-            "Not signed in. Please run 'codex login' to sign in with ChatGPT, then re-run 'codex cloud'."
-        );
-        std::process::exit(1);
+    let auth_manager = util::load_auth_manager().await;
+    let auth = match auth_manager.as_ref() {
+        Some(manager) => manager.auth().await,
+        None => None,
     };
-    let Some(auth) = auth_manager.auth().await else {
-        eprintln!(
-            "Not signed in. Please run 'codex login' to sign in with ChatGPT, then re-run 'codex cloud'."
-        );
-        std::process::exit(1);
+    let auth = match auth {
+        Some(auth) => auth,
+        None => {
+            eprintln!(
+                "Not signed in. Please run 'codex login' to sign in with ChatGPT, then re-run 'codex cloud'."
+            );
+            std::process::exit(1);
+        }
     };
 
     if let Some(acc) = auth.get_account_id() {
         append_error_log(format!("auth: mode=ChatGPT account_id={acc}"));
     }
 
-    let authorization_header_value = auth_manager
-        .chatgpt_authorization_header_for_auth(&auth)
-        .await;
-    let Some(authorization_header_value) = authorization_header_value else {
-        eprintln!(
-            "Not signed in. Please run 'codex login' to sign in with ChatGPT, then re-run 'codex cloud'."
-        );
-        std::process::exit(1);
+    let token = match auth.get_token() {
+        Ok(t) if !t.is_empty() => t,
+        _ => {
+            eprintln!(
+                "Not signed in. Please run 'codex login' to sign in with ChatGPT, then re-run 'codex cloud'."
+            );
+            std::process::exit(1);
+        }
     };
 
-    http = http.with_authorization_header_value(authorization_header_value);
-    if let Some(acc) = auth.get_account_id().or_else(|| {
-        auth.get_token()
-            .ok()
-            .and_then(|token| util::extract_chatgpt_account_id(&token))
-    }) {
+    http = http.with_bearer_token(token.clone());
+    if let Some(acc) = auth
+        .get_account_id()
+        .or_else(|| util::extract_chatgpt_account_id(&token))
+    {
         append_error_log(format!("auth: set ChatGPT-Account-Id header: {acc}"));
         http = http.with_chatgpt_account_id(acc);
     }
-    if auth.is_fedramp_account() {
-        http = http.with_fedramp_routing_header();
-    }
 
     Ok(BackendContext {
         backend: Arc::new(http),