Add virtual printer Queue mode and sidebar badge indicators

Virtual Printer Changes:
- Add new "Queue" mode that archives files and adds them to print queue
- Rename modes: "Immediate" → "Archive", "Queue for Review" → "Review"
- Three modes now: Archive (immediate), Review (pending), Queue (print queue)
- Queue mode creates unassigned queue items (printer_id=null)

Print Queue Changes:
- Make printer_id nullable in PrintQueueItem model/schema
- Add support for unassigned queue items (no printer assigned)
- Queue page shows "Unassigned" filter option
- Edit modal allows assigning printer to unassigned items
- Unassigned items highlighted in orange

Sidebar Badge Indicators:
- Queue icon shows yellow badge with pending queue item count
- Archive icon shows blue badge with pending upload count
- Badges auto-update every 5 seconds and on window focus

Other:
- Update backup/restore to handle nullable printer_id and ams_mapping
- Add database migration for nullable printer_id column
- Update VirtualPrinterSettings tests for new modes
- Update virtual printer API integration tests
- Remove speed controls documentation from wiki (not implemented)

backend/tests/integration/test_virtual_printer_api.py

@@ -53,11 +53,31 @@ class TestVirtualPrinterSettingsAPI:
     @pytest.mark.integration
     async def test_update_mode(self, async_client: AsyncClient):
         """Verify mode can be updated."""
+        response = await async_client.put("/api/v1/settings/virtual-printer?mode=review")
+
+        assert response.status_code == 200
+        result = response.json()
+        assert result["mode"] == "review"
+
+    @pytest.mark.asyncio
+    @pytest.mark.integration
+    async def test_update_mode_to_print_queue(self, async_client: AsyncClient):
+        """Verify mode can be set to print_queue."""
+        response = await async_client.put("/api/v1/settings/virtual-printer?mode=print_queue")
+
+        assert response.status_code == 200
+        result = response.json()
+        assert result["mode"] == "print_queue"
+
+    @pytest.mark.asyncio
+    @pytest.mark.integration
+    async def test_update_mode_legacy_queue_maps_to_review(self, async_client: AsyncClient):
+        """Verify legacy 'queue' mode is normalized to 'review'."""
         response = await async_client.put("/api/v1/settings/virtual-printer?mode=queue")
 
         assert response.status_code == 200
         result = response.json()
-        assert result["mode"] == "queue"
+        assert result["mode"] == "review"  # Legacy queue maps to review
 
     @pytest.mark.asyncio
     @pytest.mark.integration