Session list groups all clones of same repo together — confusing for multi-clone workflows

Description

When you have multiple local clones of the same repo (e.g. monorepo/, monorepo_2/, monorepo_3/), the session list in the UI groups all sessions under a single project entry. This makes it very hard to tell which session belongs to which local clone.

Comparison with Codex app

In the Codex app, each folder has its own thread, and you can open multiple sessions within each thread. This makes it easy to manage parallel workstreams — you always know which folder you're in.

In the Claude Code app, all sessions from different clones of the same repo are lumped together. When working on different tasks across different folders simultaneously, there's no way to tell which folder a session belongs to. It's very easy to mix them up and run commands in the wrong context.

Steps to reproduce

1. Clone the same repo into multiple directories (e.g. ~/src/monorepo, ~/src/monorepo_2, ~/src/monorepo_3)
2. Start Claude Code sessions in each directory
3. Open the session list

Expected behavior

Sessions should be organized by local directory path, similar to how Codex organizes by folder. Each folder should have its own grouping, with sessions nested under it. You should always be able to tell which folder a session was started in.

Actual behavior

All sessions from all clones appear grouped under a single project (based on git remote), making it impossible to tell which local directory a session belongs to.

Why this matters

Multi-clone workflows are common when:

• Running parallel workstreams on the same repo
• Keeping a clean clone separate from an experimental one
• Working on different tasks simultaneously across folders
• Using multiple clones as a workaround for long-running tasks

The project-scoped files (~/.claude/projects/) already distinguish between clones (separate directories per path), but the session list UI does not surface this distinction.

Suggestion

Organize sessions by local folder path (like Codex does), not just by git remote URL. Show the directory name prominently so users can immediately identify which clone a session belongs to.