[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/core/src/client.rs

@@ -2141,6 +2141,7 @@ impl AuthRequestTelemetryContext {
                 AuthMode::ApiKey | AuthMode::BedrockApiKey => "ApiKey",
                 AuthMode::Chatgpt
                 | AuthMode::ChatgptAuthTokens
+                | AuthMode::Headers
                 | AuthMode::AgentIdentity
                 | AuthMode::PersonalAccessToken => "Chatgpt",
             }),