FN-5915: show unread badge on header mailbox

Add unread mailbox status to the desktop header toggle while keeping pending approvals prioritized.

- show an unread status dot on the desktop header mailbox toggle when unread mail exists without pending approvals
- keep pending-approval indicators taking precedence and hide mailbox indicators while the mailbox view is active
- extend Header coverage for unread-only, pending-only, combined, zero-count, and active-mailbox states
- update restart integration coverage to reuse an existing worktree during orphaned resume concurrency

Files changed:
 docs/dashboard-guide.md                            |  2 +-
 packages/dashboard/app/components/Header.tsx       |  9 +++++--
 .../app/components/__tests__/Header.test.tsx       | 26 ++++++++++++++++---
 .../src/__tests__/restart.integration.test.ts      | 29 ++++++++++++++++++++--
 4 files changed, 58 insertions(+), 8 deletions(-)

Fusion-Task-Id: FN-5915

Fusion-Task-Lineage: 3a207e2c-ca58-402f-94cf-3a9e514fe263

packages/engine/src/__tests__/restart.integration.test.ts

@@ -1298,9 +1298,34 @@ describe("Crash scenario edge cases", () => {
 
   it("concurrent resumeOrphaned() calls don't double-execute the same task", async () => {
     const store = createMockStore();
-    const task = makeTask("FN-092", "in-progress");
+    const worktreePath = "/tmp/test/.worktrees/swift-falcon";
+    const task = makeTask("FN-092", "in-progress", {
+      worktree: worktreePath,
+      branch: "fusion/fn-092",
+    });
     store.listTasks.mockResolvedValue([task]);
-    store.getTask.mockResolvedValue(makeTaskDetail("FN-092", "in-progress"));
+    store.getTask.mockResolvedValue(makeTaskDetail("FN-092", "in-progress", {
+      worktree: worktreePath,
+      branch: "fusion/fn-092",
+    }));
+    mockedExecSync.mockImplementation(((cmd: unknown) => {
+      if (String(cmd) === "git rev-parse --is-inside-work-tree") {
+        return "true\n" as any;
+      }
+      if (String(cmd) === "git worktree list --porcelain") {
+        return [
+          "worktree /tmp/test",
+          "HEAD abc123",
+          "branch refs/heads/main",
+          "",
+          `worktree ${worktreePath}`,
+          "HEAD def456",
+          "branch refs/heads/fusion/fn-092",
+          "",
+        ].join("\n") as any;
+      }
+      return Buffer.from("");
+    }) as any);
 
     let resolvePrompt: (() => void) | undefined;
     mockedCreateFnAgent.mockResolvedValue({