[FEATURE] Title: Chat sessions lose working-directory context on new session — no way to spawn a new chat pre-attached to an existing project folder

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

Every new Claude Code session starts with no working directory attached ("No folder"), even when I've been working on a fixed project for days or weeks. To keep working on the same project, I have to manually repeat the reconnect-to-folder steps in every new chat — even though the project itself, on disk, hasn't changed.

Proposed Solution

Description:
Practical effect: users end up keeping a single long-running chat indefinitely just to avoid this repetitive step, which unnecessarily increases cost/latency per message (the entire conversation history is resent as context on every turn), purely to avoid losing the link to the working folder.

Proposal: a persistent "project" concept in the sidebar, with a "+ New Chat" button directly on it — any new chat started from there automatically inherits the working directory, without the manual reconnect step. Chats would stay separate (their own history), but the folder context would be shared at the project level, not tied to each individual session.

Alternative Solutions

_No response_

Priority

Critical - Blocking my work

Feature Category

CLI commands and flags

Use Case Example

_No response_

Additional Context

_No response_