Show login options when not signed in with ChatGPT (#2440)

Motivation: we have users who uses their API key although they want to
use ChatGPT account. We want to give them the chance to always login
with their account.

This PR displays login options when the user is not signed in with
ChatGPT. Even if you have set an OpenAI API key as an environment
variable, you will still be prompted to log in with ChatGPT.

We’ve also added a new flag, `always_use_api_key_signing` false by
default, which ensures you are never asked to log in with ChatGPT and
always defaults to using your API key.



https://github.com/user-attachments/assets/b61ebfa9-3c5e-4ab7-bf94-395c23a0e0af

After ChatGPT sign in:


https://github.com/user-attachments/assets/d58b366b-c46a-428f-a22f-2ac230f991c0

codex-rs/chatgpt/src/chatgpt_token.rs

@@ -1,3 +1,4 @@
+use codex_login::AuthMode;
 use codex_login::CodexAuth;
 use std::path::Path;
 use std::sync::LazyLock;
@@ -19,7 +20,7 @@ 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_codex_home(codex_home, AuthMode::ChatGPT)?;
     if let Some(auth) = auth {
         let token_data = auth.get_token_data().await?;
         set_chatgpt_token_data(token_data);