[Auth] Introduce New Auth Storage Abstraction for Codex CLI (#5569)

This PR introduces a new `Auth Storage` abstraction layer that takes
care of read, write, and load of auth tokens based on the
AuthCredentialsStoreMode. It is similar to how we handle MCP client
oauth
[here](https://github.com/openai/codex/blob/main/codex-rs/rmcp-client/src/oauth.rs).
Instead of reading and writing directly from disk for auth tokens, Codex
CLI workflows now should instead use this auth storage using the public
helper functions.

This PR is just a refactor of the current code so the behavior stays the
same. We will add support for keyring and hybrid mode in follow-up PRs.

I have read the CLA Document and I hereby sign the CLA

codex-rs/chatgpt/src/chatgpt_token.rs

@@ -19,7 +19,7 @@ pub fn set_chatgpt_token_data(value: TokenData) {
 
 /// Initialize the ChatGPT token from auth.json file
 pub async fn init_chatgpt_token_from_auth(codex_home: &Path) -> std::io::Result<()> {
-    let auth = CodexAuth::from_codex_home(codex_home)?;
+    let auth = CodexAuth::from_auth_storage(codex_home)?;
     if let Some(auth) = auth {
         let token_data = auth.get_token_data().await?;
         set_chatgpt_token_data(token_data);