feat: add search APIs and telegram-like chats sidebar flow

- implement chat query filtering and message search endpoints

- add db indexes for search fields

- activate chats search input in web

- replace inline create panel with floating TG-style action menu

app/chats/service.py

@@ -47,9 +47,16 @@ async def create_chat_for_user(db: AsyncSession, *, creator_id: int, payload: Ch
     return chat
 
 
-async def get_chats_for_user(db: AsyncSession, *, user_id: int, limit: int = 50, before_id: int | None = None) -> list[Chat]:
+async def get_chats_for_user(
+    db: AsyncSession,
+    *,
+    user_id: int,
+    limit: int = 50,
+    before_id: int | None = None,
+    query: str | None = None,
+) -> list[Chat]:
     safe_limit = max(1, min(limit, 100))
-    return await repository.list_user_chats(db, user_id=user_id, limit=safe_limit, before_id=before_id)
+    return await repository.list_user_chats(db, user_id=user_id, limit=safe_limit, before_id=before_id, query=query)
 
 
 async def get_chat_for_user(db: AsyncSession, *, chat_id: int, user_id: int) -> tuple[Chat, list]: