Add native Google Chat connector now that Google has now published an official Chat MCP server

### Problem Statement

I'm trying to let Claude read my team's Google Chat (search and read messages and spaces), but Claude's native Google Workspace connectors currently cover only Gmail, Calendar, and Drive: Google Chat is not included.

A prior request for this, #138, was closed as "not planned" on 2026-04-02. That was *before* Google published its official Chat MCP server, so the situation has materially changed and I think it's worth revisiting.

### Proposed Solution

Add Google Chat as a native, ready-to-use Workspace connector alongside the existing Gmail/Drive/Calendar connectors. Read-only to start (search/list/read messages and spaces) would cover the most common use cases; send-message could follow.

Google has already done much of the groundwork — there is now an official, first-party Google Chat remote MCP server:
- Chat MCP server docs: https://developers.google.com/workspace/chat/api/guides/configure-mcp-server
- Workspace MCP servers overview: https://developers.google.com/workspace/guides/configure-mcp-servers
- Endpoint: `https://chatmcp.googleapis.com/mcp/v1`
- The docs already list `https://claude.ai/api/mcp/auth_callback` as a supported OAuth redirect URI — i.e. Claude is explicitly a target client.

### Alternatives Considered

Today the official Google Chat MCP server can be added to Claude as a custom connector, but it requires each user/org to stand up their own Google Cloud project, enable two APIs, configure an OAuth consent screen, and create an OAuth client. Open-source self-hosted servers exist but carry the same setup burden plus third-party-trust concerns. A native connector could make this fairly seamless, much like the Drive and Gmail connectors already do.

### Area

MCP Connector (adding/managing servers)

### Priority

High - Major improvement needed

### Additional Context

Follow-up to #138 (closed before Google's server existed).