[Remote] Assistant sessions display the wrong workspace and branch

## Bug
When opening a Claw assistant session in BitFun Remote, the header displays `home / master`.

## Expected behavior
Assistant/Claw sessions should show the assistant context, or omit repository workspace and branch information when no Git workspace is attached.

## Actual behavior
The remote web UI keeps displaying the previously selected normal workspace (`home`) and its branch (`master`). This is misleading, although command execution appears to use the correct assistant workspace.

## Reproduction
1. Open BitFun Remote with a normal workspace selected.
2. Switch to Assistant mode.
3. Open a Claw assistant session.
4. Observe the session header: it still shows the normal workspace and branch.

## Environment
- BitFun 0.2.17
- macOS desktop client
- BitFun Remote web UI via relay

## Additional evidence
The Claw session target is the dedicated assistant workspace (`~/.bitfun/personal_assistant/workspace`), which is not a Git repository. The desktop runtime logs also report that assistant session commands use that path, so this appears to be stale web UI state rather than backend routing to the normal workspace.

Reproduisez ceci dans l’interface web de BitFun Remote en sélectionnant un Workspace normal, en passant en mode Assistant et en ouvrant une session Claw. Suivez la manière dont l’en-tête de session conserve l’état du Workspace et de la branche ; le travail est terminé lorsque le contexte de l’Assistant est affiché ou que les champs du dépôt sont omis, sans modifier le comportement du Workspace normal.

Rédigé par le modèle d'indexation à partir du texte de l'issue.