[Bug] tabs_context_mcp browser extension connection fails until Chrome restart within session

Bug Description
tabs_context_mcp always fails with "Browser extension is not connected" regardless of launch order. Connection only succeeds after restarting Chrome from within an active Claude Code session.

Tested scenarios (all fail):

• Chrome running → Start Claude Code
• Quit Chrome → Start Claude Code → Launch Chrome
• Start Claude Code → Call tabs_context_mcp (to start MCP server) → Launch Chrome

Workaround (not a fix):
Restart Chrome via osascript from within the session. This must be done every session.

Environment: macOS 15.2, Claude Code 2.0.76, Extension 1.0.36

Environment Info

• Platform: darwin
• Terminal: ghostty
• Version: 2.0.76
• Feedback ID: af0e54a4-f494-48df-af1b-5be9f12ad66d

Errors

[{"error":"Error: Tool mcp__claude-in-chrome__tabs_context_mcp not found\n    at WwB (/$bunfs/root/claude:2541:6724)\n    at L4 (/$bunfs/root/claude:202:20697)\n    at wq (/$bunfs/root/claude:202:39069)\n    at DTT (/$bunfs/root/claude:202:49684)\n    at J6 (/$bunfs/root/claude:202:85872)\n    at Vv (/$bunfs/root/claude:202:84850)\n    at mf (/$bunfs/root/claude:202:84675)\n    at Hk (/$bunfs/root/claude:202:81115)\n    at lA (/$bunfs/root/claude:202:6242)\n    at qoR (/$bunfs/root/claude:195:4072)","timestamp":"2025-12-27T18:49:21.580Z"},{"error":"Error: Tool mcp__claude-in-chrome__tabs_context_mcp not found\n    at WwB (/$bunfs/root/claude:2541:6724)\n    at L4 (/$bunfs/root/claude:202:20697)\n    at wq (/$bunfs/root/claude:202:39069)\n    at DTT (/$bunfs/root/claude:202:49684)\n    at J6 (/$bunfs/root/claude:202:85872)\n    at Vv (/$bunfs/root/claude:202:84850)\n    at mf (/$bunfs/root/claude:202:84675)\n    at Hk (/$bunfs/root/claude:202:81115)\n    at lA (/$bunfs/root/claude:202:6242)\n    at qoR (/$bunfs/root/claude:195:4072)","timestamp":"2025-12-27T18:49:21.588Z"},{"error":"Error: Tool mcp__claude-in-chrome__navigate not found\n    at WwB (/$bunfs/root/claude:2541:6724)\n    at L4 (/$bunfs/root/claude:202:20697)\n    at wq (/$bunfs/root/claude:202:39069)\n    at DTT (/$bunfs/root/claude:202:49684)\n    at J6 (/$bunfs/root/claude:202:85872)\n    at Vv (/$bunfs/root/claude:202:84850)\n    at mf (/$bunfs/root/claude:202:84675)\n    at Hk (/$bunfs/root/claude:202:81115)\n    at lA (/$bunfs/root/claude:202:6242)\n    at qoR (/$bunfs/root/claude:195:4072)","timestamp":"2025-12-27T18:49:21.588Z"},{"error":"Error: Tool mcp__claude-in-chrome__computer not found\n    at WwB (/$bunfs/root/claude:2541:6724)\n    at L4 (/$bunfs/root/claude:202:20697)\n    at wq (/$bunfs/root/claude:202:39069)\n    at DTT (/$bunfs/root/claude:202:49684)\n    at J6 (/$bunfs/root/claude:202:85872)\n    at Vv (/$bunfs/root/claude:202:84850)\n    at mf (/$bunfs/root/claude:202:84675)\n    at Hk (/$bunfs/root/claude:202:81115)\n    at lA (/$bunfs/root/claude:202:6242)\n    at qoR (/$bunfs/root/claude:195:4072)","timestamp":"2025-12-27T18:49:21.588Z"}]