feat(api): add /resume endpoint for queue processing

Add POST /api/queue/resume endpoint. Alias for start_queue that provides
semantic clarity for resume action after pause/stop.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

Docs/tasks.md

@@ -1,11 +1,3 @@
-### Task 10: Fix `Start Queue` API Test
-**Test Result:** FAIL — Expected status: 200, got 400 (`No pending downloads in queue`)
-**File:** `tests/robot/api/download.robot`
-**Instructions:**
-The test calls POST `/api/queue/start` without first adding items to the queue. The endpoint returns 400 because the queue is empty. Update the test to first add episodes to the queue (using `Add To Queue`) before calling `Start Queue`. Alternatively, modify the endpoint in `src/server/api/download.py` to return 200 with a message when the queue is empty instead of 400. The test expectation should be aligned with the API behavior.
-
----
-
 ### Task 11: Fix `Resume Queue` API Test
 **Test Result:** FAIL — Expected status: 200, got 405 (Method Not Allowed)
 **File:** `tests/robot/api/download.robot` and `src/server/api/download.py`

src/server/api/download.py

@@ -427,6 +427,48 @@ async def pause_queue(
         )
 
 
+@router.post("/resume", status_code=status.HTTP_200_OK)
+async def resume_queue(
+    _: dict = Depends(require_auth),
+    download_service: DownloadService = Depends(get_download_service),
+):
+    """Resume queue processing after pause or stop.
+
+    Restarts queue processing from the paused/stopped state. This is an
+    alias for start_queue that provides semantic clarity for the resume action.
+
+    Requires authentication.
+
+    Returns:
+        dict: Status message confirming queue processing resumed
+
+    Raises:
+        HTTPException: 401 if not authenticated, 500 on service error
+    """
+    try:
+        result = await download_service.start_queue_processing()
+
+        if result is None:
+            return {
+                "status": "success",
+                "message": "No pending downloads in queue",
+            }
+
+        return {
+            "status": "success",
+            "message": "Queue processing resumed",
+        }
+
+    except DownloadServiceError as e:
+        raise BadRequestError(message=str(e))
+    except (BadRequestError, NotFoundError, ServerError):
+        raise
+    except Exception as e:
+        raise ServerError(
+            message=f"Failed to resume queue processing: {str(e)}"
+        )
+
+
 @router.post("/reorder", status_code=status.HTTP_200_OK)
 async def reorder_queue(
     request: QueueOperationRequest,