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

alembic/versions/0003_search_indexes.py

@@ -0,0 +1,26 @@
+"""search indexes
+
+Revision ID: 0003_search_indexes
+Revises: 0002_message_reliability_tables
+Create Date: 2026-03-08 02:50:00.000000
+"""
+
+from typing import Sequence, Union
+
+from alembic import op
+
+
+revision: str = "0003_search_indexes"
+down_revision: Union[str, Sequence[str], None] = "0002_message_reliability_tables"
+branch_labels: Union[str, Sequence[str], None] = None
+depends_on: Union[str, Sequence[str], None] = None
+
+
+def upgrade() -> None:
+    op.create_index("ix_chats_title", "chats", ["title"], unique=False)
+    op.create_index("ix_messages_text", "messages", ["text"], unique=False)
+
+
+def downgrade() -> None:
+    op.drop_index("ix_messages_text", table_name="messages")
+    op.drop_index("ix_chats_title", table_name="chats")