[Feature Request] Add integration with Claude Web projects and chat history for local Claude Code access

Bug Description
Could Claude Code running locally be connected to my Claude Web because I have some projects that I created in Claude Web and have a lot of chats in there? It creates a memory for that specific project. For a specific business use case I asked all my business questions in that project. At times when I'm building something here in Claude Code I would want to pull context from that, be able to search my historical chats and see my memory and any files that I have attached in that project to answer questions in here. Please add that functionality.

Environment Info

• Platform: darwin
• Terminal: xterm-256color
• Version: 2.1.179
• Feedback ID: 204daca0-4cb8-495d-b4c4-4bee710abec7

Errors

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