feat: add Bedrock API key as a managed auth mode (#27443)

## Why

Codex needs to manage Amazon Bedrock API key credentials through the
existing auth lifecycle instead of introducing a separate auth manager
or provider-specific credential file. Treating Bedrock API key login as
a primary auth mode gives it the same persistence, keyring, reload, and
logout behavior as the existing OpenAI API key and ChatGPT modes.

The credential is valid only for the `amazon-bedrock` model provider.
OpenAI-compatible providers must reject this auth mode rather than
treating the Bedrock key as an OpenAI bearer token.

## What changed

- Added `bedrockApiKey` as an app-server `AuthMode` and
`CodexAuth::BedrockApiKey` as a primary `AuthManager` mode.
- Added `BedrockApiKeyAuth`, containing the API key and AWS region, to
the existing `AuthDotJson` payload stored in `$CODEX_HOME/auth.json` or
the configured keyring backend.
- Added `login_with_bedrock_api_key(...)`, parallel to
`login_with_api_key(...)`, which replaces the current stored login with
Bedrock credentials.
- Reused generic auth reload and logout behavior instead of adding a
Bedrock-specific auth manager or logout path.
- Updated login restrictions, status reporting, diagnostics, telemetry
classification, generated app-server schemas, and auth fixtures for the
new mode.
- Added explicit errors when Bedrock API key auth is selected with an
OpenAI-compatible model provider.

This PR establishes managed storage and auth-mode behavior. Routing the
managed key and region into Amazon Bedrock requests will be in follow-up
PRs.

codex-rs/core/src/client.rs

@@ -1985,7 +1985,7 @@ impl AuthRequestTelemetryContext {
         let auth_telemetry = auth_header_telemetry(api_auth);
         Self {
             auth_mode: auth_mode.map(|mode| match mode {
-                AuthMode::ApiKey => "ApiKey",
+                AuthMode::ApiKey | AuthMode::BedrockApiKey => "ApiKey",
                 AuthMode::Chatgpt
                 | AuthMode::ChatgptAuthTokens
                 | AuthMode::AgentIdentity