Desktop app sidebar shows project groups as empty despite session transcripts existing on disk

**Description**

In the Claude Code desktop app, several project groups in the sidebar (FlowPilot, GnP, AuditOS App) render as empty ("Drag or move sessions here"), even though real session transcripts exist on disk for each project under `~/.claude/projects//*.jsonl`.

**Evidence gathered**

| Sidebar group | Project folder | Session files on disk |
|---|---|---|
| FlowPilot | SME-Operation-App | 12 |
| GnP | Guuru-and-Pundeet | 1 |
| AuditOS App | Internal-Audit-App | 4 |
| Sabbi | Sabbi | 1 (sidebar shows 2 entries under this group) |

- The sidebar's "Ungrouped" section shows 4 sessions that also aren't reflected by the app's own session-management tooling.
- Querying the app's session list via its MCP session-management tool (`list_sessions`) returned "No other sessions found" — despite the sidebar visibly showing multiple sessions (Ungrouped + Sabbi).
- A full quit-and-relaunch of the desktop app did NOT resolve the issue — the same groups remained empty afterward.

**Expected behavior**

Sessions with transcript files on disk for a given project should appear grouped under that project in the sidebar after restart, matching what's actually stored locally.

**Actual behavior**

Project groups (FlowPilot, GnP, AuditOS App) show as empty despite having session data on disk. The app's internal session index appears out of sync with the on-disk transcripts, and this persists across restarts.

**Environment**

- OS: Windows 11 Pro
- Product: Claude Code desktop app

Reproduce on Windows 11 using the listed project folders under ~/.claude/projects//*.jsonl, then compare the desktop sidebar with the list_sessions MCP result before and after a full restart. Trace the session indexing and project-group loading path; done means existing transcripts appear under the correct groups and list_sessions matches the visible sessions.

Written by the indexing model from the issue text.