refactor: route Codex auth through AuthProvider (#18811)

## Summary

This PR moves Codex backend request authentication from direct
bearer-token handling to `AuthProvider`.

The new `codex-auth-provider` crate defines the shared request-auth
trait. `CodexAuth::provider()` returns a provider that can apply all
headers needed for the selected auth mode.

This lets ChatGPT token auth and AgentIdentity auth share the same
callsite path:
- ChatGPT token auth applies bearer auth plus account/FedRAMP headers
where needed.
- AgentIdentity auth applies AgentAssertion plus account/FedRAMP headers
where needed.

Reference old stack: https://github.com/openai/codex/pull/17387/changes

## Callsite Migration

| Area | Change |
| --- | --- |
| backend-client | accepts an `AuthProvider` instead of a raw
token/header |
| chatgpt client/connectors | applies auth through
`CodexAuth::provider()` |
| cloud tasks | keeps Codex-backend gating, applies auth through
provider |
| cloud requirements | uses Codex-backend auth checks and provider
headers |
| app-server remote control | applies provider headers for backend calls
|
| MCP Apps/connectors | gates on `uses_codex_backend()` and keys caches
from generic account getters |
| model refresh | treats AgentIdentity as Codex-backend auth |
| OpenAI file upload path | rejects non-Codex-backend auth before
applying headers |
| core client setup | keeps model-provider auth flow and allows
AgentIdentity through provider-backed OpenAI auth |

## Stack

1. https://github.com/openai/codex/pull/18757: full revert
2. https://github.com/openai/codex/pull/18871: isolated Agent Identity
crate
3. https://github.com/openai/codex/pull/18785: explicit AgentIdentity
auth mode and startup task allocation
4. This PR: migrate Codex backend auth callsites through AuthProvider
5. https://github.com/openai/codex/pull/18904: accept AgentIdentity JWTs
and load `CODEX_AGENT_IDENTITY`

## Testing

Tests: targeted Rust checks, cargo-shear, Bazel lock check, and CI.

codex-rs/chatgpt/src/apply_command.rs

@@ -6,7 +6,6 @@ use codex_git_utils::ApplyGitRequest;
 use codex_git_utils::apply_git_patch;
 use codex_utils_cli::CliConfigOverrides;
 
-use crate::chatgpt_token::init_chatgpt_token_from_auth;
 use crate::get_task::GetTaskResponse;
 use crate::get_task::OutputItem;
 use crate::get_task::PrOutputItem;
@@ -32,9 +31,6 @@ pub async fn run_apply_command(
     )
     .await?;
 
-    init_chatgpt_token_from_auth(&config.codex_home, config.cli_auth_credentials_store_mode)
-        .await?;
-
     let task_response = get_task(&config, apply_cli.task_id).await?;
     apply_diff_from_task(task_response, cwd).await
 }