[connectors] Support connectors part 1 - App server & MCP (#9667)

In order to make Codex work with connectors, we add a built-in gateway
MCP that acts as a transparent proxy between the client and the
connectors. The gateway MCP collects actions that are accessible to the
user and sends them down to the user, when a connector action is chosen
to be called, the client invokes the action through the gateway MCP as
well.

 - [x] Add the system built-in gateway MCP to list and run connectors.
 - [x] Add the app server methods and protocol

codex-rs/app-server/README.md

@@ -89,6 +89,7 @@ Example (from OpenAI's official VSCode extension):
 - `model/list` — list available models (with reasoning effort options).
 - `collaborationMode/list` — list available collaboration mode presets (experimental, no pagination).
 - `skills/list` — list skills for one or more `cwd` values (optional `forceReload`).
+- `app/list` — list available apps.
 - `skills/config/write` — write user-level skill config by path.
 - `mcpServer/oauth/login` — start an OAuth login for a configured MCP server; returns an `authorization_url` and later emits `mcpServer/oauthLogin/completed` once the browser flow finishes.
 - `tool/requestUserInput` — prompt the user with 1–3 short questions for a tool call and return their answers (experimental).