Simplify auth flow and reconcile differences between ChatGPT and API Key auth (#3189)

This PR does the following:
* Adds the ability to paste or type an API key.
* Removes the `preferred_auth_method` config option. The last login
method is always persisted in auth.json, so this isn't needed.
* If OPENAI_API_KEY env variable is defined, the value is used to
prepopulate the new UI. The env variable is otherwise ignored by the
CLI.
* Adds a new MCP server entry point "login_api_key" so we can implement
this same API key behavior for the VS Code extension.
<img width="473" height="140" alt="Screenshot 2025-09-04 at 3 51 04 PM"
src="https://github.com/user-attachments/assets/c11bbd5b-8a4d-4d71-90fd-34130460f9d9"
/>
<img width="726" height="254" alt="Screenshot 2025-09-04 at 3 51 32 PM"
src="https://github.com/user-attachments/assets/6cc76b34-309a-4387-acbc-15ee5c756db9"
/>

codex-rs/exec/src/lib.rs

@@ -187,10 +187,8 @@ pub async fn run_main(cli: Cli, codex_linux_sandbox_exe: Option<PathBuf>) -> any
         std::process::exit(1);
     }
 
-    let conversation_manager = ConversationManager::new(AuthManager::shared(
-        config.codex_home.clone(),
-        config.preferred_auth_method,
-    ));
+    let conversation_manager =
+        ConversationManager::new(AuthManager::shared(config.codex_home.clone()));
     let NewConversation {
         conversation_id: _,
         conversation,