[codex] Add externally provided Codex auth (#31274)

## Summary

Add an in-memory externally provided Codex auth snapshot with explicit
runtime capabilities, installed through the existing `ExternalAuth`
provider path.

## Testing

- `just fmt-check`
- `cargo test -p codex-login --lib externally_provided_auth`
- `cargo test -p codex-core --lib
external_auth_snapshot_is_installed_from_runtime_config`
- `cargo test -p codex-model-provider --lib external_auth`
- `cargo test -p codex-mcp-extension --test hosted_apps_mcp
hosted_apps_mcp_accepts_external_provided_codex_auth`
- `cargo check -p codex-app-server -p codex-core-api -p
codex-thread-manager-sample`

---------

Co-authored-by: pakrym-oai <pakrym@openai.com>

codex-rs/app-server/src/request_processors/account_processor.rs

@@ -855,7 +855,9 @@ impl AccountRequestProcessor {
                     let auth_mode = auth_mode_to_api(auth.api_auth_mode());
                     let (reported_auth_method, token_opt) = if matches!(
                         auth,
-                        CodexAuth::AgentIdentity(_) | CodexAuth::PersonalAccessToken(_)
+                        CodexAuth::Headers(_)
+                            | CodexAuth::AgentIdentity(_)
+                            | CodexAuth::PersonalAccessToken(_)
                     ) || include_token
                         && permanent_refresh_failure
                     {