Add updated_at and created_at to Playlist model

Introduces created_at and updated_at fields to the Playlist model for tracking creation and modification times. Refactors room user removal logic to handle owner transfer and participant count updates more robustly. Updates room query logic for more accurate filtering by category and status. Adds migration stubs for updated_at column in room playlists.

app/database/playlists.py

@@ -1,5 +1,5 @@
 from datetime import datetime
-from typing import TYPE_CHECKING
+from typing import TYPE_CHECKING, Optional
 
 from app.models.model import UTCBaseModel
 from app.models.mods import APIMod
@@ -60,6 +60,17 @@ class Playlist(PlaylistBase, table=True):
         }
     )
     room: "Room" = Relationship()
+    created_at: Optional[datetime] = Field(
+        default=None, 
+        sa_column_kwargs={"server_default": func.now()}
+    )
+    updated_at: Optional[datetime] = Field(
+        default=None,
+        sa_column_kwargs={
+            "server_default": func.now(),
+            "onupdate": func.now()
+        }
+    )
 
     @classmethod
     async def get_next_id_for_room(cls, room_id: int, session: AsyncSession) -> int: