claude-in-chrome: 'No Chrome extension connected' is a misleading error when tab group doesn't exist

Bug Description

The tabs_context_mcp tool returns "No Chrome extension connected" even when the Claude browser extension IS installed, connected, and visible in the Chrome toolbar. The actual problem is that no MCP tab group exists yet — which is a completely different condition.

Steps to Reproduce

1. Install the Claude browser extension and connect it to Claude Code
2. Call tabs_context_mcp() (without createIfEmpty: true) at the start of a session
3. Receive: "No Chrome extension connected."
4. Call tabs_context_mcp(createIfEmpty: true)
5. Success — tabs are returned and everything works

Expected Behavior

• "No Chrome extension connected" should only appear when the extension is genuinely not connected
• When no tab group exists but the extension IS connected, the error should say something like: "No MCP tab group found. Call tabs_context_mcp with createIfEmpty: true to create one."
• Or ideally, tabs_context_mcp() without createIfEmpty should still work if the extension is connected

Actual Behavior

The same error message is used for two distinct states:

1. Extension not installed/connected at all
2. Extension connected but no MCP tab group exists

This causes users to think the extension is broken, triggers unnecessary reconnection attempts, and hides the actual fix (createIfEmpty: true).

Impact

• Users waste time reconnecting/reinstalling the extension when it was already working
• The actual fix (tabs_context_mcp with createIfEmpty: true) is not surfaced in the error message
• Automated agents following the error message instructions go in circles

Suggested Fix

1. Distinguish the two error states with different messages
2. When tab group is missing but extension is connected, suggest createIfEmpty: true in the error
3. Or: make createIfEmpty: true the default behavior of tabs_context_mcp

Environment

• Claude Code (claude-in-chrome MCP tools)
• macOS 24.6.0 (Darwin)
• Chrome with Claude extension installed