add inventory sorting to the api

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>

trade-hub/backend/app/inventory.py

@@ -75,10 +75,35 @@ def _find(db: DbSession, user: User, class_name: str) -> InventoryEntry | None:
     ).scalar_one_or_none()
 
 
+def _sort_key_name(item):
+    return (item["name"].lower(), item["class_name"])
+
+
+def _sort_key_category(item):
+    return ((item["category"] or "").lower(), item["name"].lower(), item["class_name"])
+
+
+def _sort_key_quantity(item):
+    return (-item["quantity"], item["name"].lower(), item["class_name"])
+
+
+def _sort_key_updated(item):
+    return (-item["updated_at"].timestamp(), item["name"].lower())
+
+
+_SORT_KEYS = {
+    "name": _sort_key_name,
+    "category": _sort_key_category,
+    "quantity": _sort_key_quantity,
+    "updated": _sort_key_updated,
+}
+
+
 @router.get("", response_model=InventoryPage)
 def list_inventory(
     category: str | None = None,
     search: str | None = None,
+    sort: str = Query(default="name", pattern="^(name|category|quantity|updated)$"),
     page: int = Query(default=1, ge=1),
     page_size: int = Query(default=25, ge=1),
     user: User = Depends(get_current_user),
@@ -102,7 +127,7 @@ def list_inventory(
             if needle in i["name"].lower() or needle in i["class_name"].lower()
         ]
 
-    items.sort(key=lambda i: (i["name"].lower(), i["class_name"]))
+    items.sort(key=_SORT_KEYS[sort])
     total = len(items)
     total_pages = max(1, math.ceil(total / page_size))
     start = (page - 1) * page_size