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/core/src/config/mod.rs

@@ -51,7 +51,7 @@ use codex_config::types::UriBasedFileOpener;
 use codex_config::types::WindowsSandboxModeToml;
 use codex_exec_server::ExecutorFileSystem;
 use codex_exec_server::LOCAL_FS;
-pub use codex_features::Feature;
+use codex_features::Feature;
 use codex_features::FeatureConfigSource;
 use codex_features::FeatureOverrides;
 use codex_features::FeatureToml;
@@ -60,7 +60,6 @@ use codex_features::FeaturesToml;
 use codex_features::MultiAgentV2ConfigToml;
 use codex_git_utils::resolve_root_git_project_for_trust;
 use codex_login::AuthManagerConfig;
-use codex_login::BackgroundAgentTaskAuthMode;
 use codex_mcp::McpConfig;
 use codex_model_provider_info::LEGACY_OLLAMA_CHAT_PROVIDER_ID;
 use codex_model_provider_info::ModelProviderInfo;
@@ -635,16 +634,6 @@ impl AuthManagerConfig for Config {
     fn forced_chatgpt_workspace_id(&self) -> Option<String> {
         self.forced_chatgpt_workspace_id.clone()
     }
-
-    fn chatgpt_base_url(&self) -> Option<String> {
-        Some(self.chatgpt_base_url.clone())
-    }
-
-    fn background_agent_task_auth_mode(&self) -> BackgroundAgentTaskAuthMode {
-        BackgroundAgentTaskAuthMode::from_feature_enabled(
-            self.features.enabled(Feature::UseAgentIdentity),
-        )
-    }
 }
 
 #[derive(Clone)]