auth: let AuthManager own external bearer auth (#16287)

## Summary

`AuthManager` and `UnauthorizedRecovery` already own token resolution
and staged `401` recovery. The missing piece for provider auth was a
bearer-only mode that still fit that design, instead of pushing a second
auth abstraction into `codex-core`.

This PR keeps the design centered on `AuthManager`: it teaches
`codex-login` how to own external bearer auth directly so later provider
work can keep calling `AuthManager.auth()` and `UnauthorizedRecovery`.

## Motivation

This is the middle layer for #15189.

The intended design is still:

- `AuthManager` encapsulates token storage and refresh
- `UnauthorizedRecovery` powers staged `401` recovery
- all request tokens go through `AuthManager.auth()`

This PR makes that possible for provider-backed bearer tokens by adding
a bearer-only auth mode inside `AuthManager` instead of building
parallel request-auth plumbing in `core`.

## What Changed

- move `ModelProviderAuthInfo` into `codex-protocol` so `core` and
`login` share one config shape
- add `login/src/auth/external_bearer.rs`, which runs the configured
command, caches the bearer token in memory, and refreshes it after `401`
- add `AuthManager::external_bearer_only(...)` for provider-scoped
request paths that should use command-backed bearer auth without
mutating the shared OpenAI auth manager
- add `AuthManager::shared_with_external_chatgpt_auth_refresher(...)`
and rename the other `AuthManager` helpers that only apply to external
ChatGPT auth so the ChatGPT-only path is explicit at the call site
- keep external ChatGPT refresh behavior unchanged while ensuring
bearer-only external auth never persists to `auth.json`

## Testing

- `cargo test -p codex-login`
- `cargo test -p codex-protocol`





---
[//]: # (BEGIN SAPLING FOOTER)
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with [ReviewStack](https://reviewstack.dev/openai/codex/pull/16287).
* #16288
* __->__ #16287

codex-rs/app-server/src/codex_message_processor.rs

@@ -1015,7 +1015,7 @@ impl CodexMessageProcessor {
         &mut self,
         params: &LoginApiKeyParams,
     ) -> std::result::Result<(), JSONRPCErrorError> {
-        if self.auth_manager.is_external_auth_active() {
+        if self.auth_manager.is_external_chatgpt_auth_active() {
             return Err(self.external_auth_active_error());
         }
 
@@ -1094,7 +1094,7 @@ impl CodexMessageProcessor {
     ) -> std::result::Result<LoginServerOptions, JSONRPCErrorError> {
         let config = self.config.as_ref();
 
-        if self.auth_manager.is_external_auth_active() {
+        if self.auth_manager.is_external_chatgpt_auth_active() {
             return Err(self.external_auth_active_error());
         }
 
@@ -1531,7 +1531,7 @@ impl CodexMessageProcessor {
     }
 
     async fn refresh_token_if_requested(&self, do_refresh: bool) -> RefreshTokenRequestOutcome {
-        if self.auth_manager.is_external_auth_active() {
+        if self.auth_manager.is_external_chatgpt_auth_active() {
             return RefreshTokenRequestOutcome::NotAttemptedOrSucceeded;
         }
         if do_refresh && let Err(err) = self.auth_manager.refresh_token().await {