[FEATURE] Desktop app: allow moving a Code session into a Claude Project

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

In the macOS desktop app, the </> Code tab lists sessions organized in groups. When a session is started from inside a Claude Project, it is linked to that project automatically — which is great. But sessions created outside a project can never be associated with one afterwards.

The context menu on a session (⋮) currently offers "Open in", "Pin", "Rename", "Fork", "Move to group", "Archive" and "Delete" — but there is no "Move to project".

Many users have accumulated dozens of Code sessions in plain groups that conceptually belong to Claude Projects, with no way to attach them retroactively.

Proposed Solution

Add a "Move to project" option to the session context menu (⋮) in the </> Code tab, next to "Move to group". Selecting it would show the list of the user's Claude Projects and attach the session (and its code/artifacts) to the chosen project — the same link that is created automatically when a session is started from inside a project.

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

Other

Use Case Example

Example scenario:

1. I use the desktop app daily and organize Code sessions into groups per client (e.g. one group per customer).
2. Later I create a Claude Project for one of those clients to centralize context, files and instructions.
3. All the existing sessions for that client remain in the plain group — there is no way to move them into the new project.
4. With a "Move to project" option in the session's ⋮ menu, I could attach those historical sessions to the project so everything about that client lives in one place.

Additional Context

_No response_