[Auto] Implement Update Todo endpoint (PATCH /todos/:id)

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+# Implement Update Todo endpoint (PATCH /todos/:id)
+
+Implement PATCH /todos/:id to partially update a Todo. Accept optional fields `title` (string, non-empty) and `completed` (boolean). Response should be 200 OK with the updated Todo object, or 404 Not Found if the id does not exist. updatedAt should be refreshed on every successful update.
+
+Acceptance Criteria:
+- Updating only title changes title and updatedAt
+- Updating only completed changes completed and updatedAt
+- Updating both fields changes both and updatedAt
+- Returns 404 for non-existent id
+- Returns 400 if title is provided as empty string
+
+Test Cases:
+- Integration: PATCH /todos/:id { "title": "New title" } returns updated Todo with new title and updated updatedAt
+- Integration: PATCH /todos/:id { "completed": true } returns updated Todo with completed=true
+- Integration: PATCH /todos/:id { "title": "A", "completed": false } returns updated Todo
+- Integration: PATCH /todos/:id with non-existent id returns 404
+- Integration: PATCH /todos/:id { "title": "" } returns 400
+- Edge: PATCH /todos/:id with {} returns 200 and Todo unchanged (or 400 depending on strictness; document behavior)
+
+Please implement this fix.