[FEATURE] Claude Code Desktop: Add "New session" shortcut per project in the sidebar

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

When working with multiple local projects simultaneously, clicking the global
"+ New session" button defaults to the last used directory — not necessarily
the project I want. I have to manually switch folders even when the target
project is already visible in the sidebar.

Proposed Solution

The sidebar should show a "+" button on each project row when hovering.
Clicking it would immediately start a new session in that project's directory,
with no folder picker required.

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

Performance and speed

Use Case Example

_No response_

Additional Context

_No response_