[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/tui/src/lib.rs

@@ -476,7 +476,7 @@ fn get_login_status(config: &Config) -> LoginStatus {
         // Reading the OpenAI API key is an async operation because it may need
         // to refresh the token. Block on it.
         let codex_home = config.codex_home.clone();
-        match CodexAuth::from_codex_home(&codex_home) {
+        match CodexAuth::from_auth_storage(&codex_home) {
             Ok(Some(auth)) => LoginStatus::AuthMode(auth.mode),
             Ok(None) => LoginStatus::NotAuthenticated,
             Err(err) => {