feat: add background information field to room model

- Add background_information field to Room database table and model
- Create database migration for the new field
- Update API schemas (CreateRoom, UpdateRoom) to handle background_information
- Integrate room context into AI summarization prompts
- Add background_information field to frontend room form
- Update TypeScript types from regenerated OpenAPI spec

The background information will be used to provide context for AI-generated
summaries, helping create more appropriate and relevant meeting summaries.

🤖 Generated with [opencode](https://opencode.ai)

Co-Authored-By: opencode <noreply@opencode.ai>

server/migrations/versions/082fa608201c_add_room_background_information.py

@@ -0,0 +1,26 @@
+"""add_room_background_information
+
+Revision ID: 082fa608201c
+Revises: b7df9609542c
+Create Date: 2025-07-29 01:41:37.912195
+
+"""
+from typing import Sequence, Union
+
+from alembic import op
+import sqlalchemy as sa
+
+
+# revision identifiers, used by Alembic.
+revision: str = '082fa608201c'
+down_revision: Union[str, None] = 'b7df9609542c'
+branch_labels: Union[str, Sequence[str], None] = None
+depends_on: Union[str, Sequence[str], None] = None
+
+
+def upgrade() -> None:
+    op.add_column('room', sa.Column('background_information', sa.Text(), nullable=True))
+
+
+def downgrade() -> None:
+    op.drop_column('room', 'background_information')