[Backend]: Persist chat-generated itineraries to trips tables

[Hanseooo]

Problem

Generated itineraries are returned to the frontend but are not persisted as durable trip records. Users cannot reliably find generated plans in trips pages after chat completion.

Context

• Reference: docs/FUTURE_ISSUES_BACKLOG.md
• Related code: backend/app/services/chat_service.py, backend/app/repositories/trip_repo.py, backend/app/models/trip.py

Requirements

• Persist generated itinerary output into Trip, TripDay, and Activity tables.
• Link persisted records to authenticated user context when available.
• Return persisted identifiers/metadata needed by frontend navigation (for example trip_id).
• Ensure failure paths do not leave partial or inconsistent records.

Acceptance Criteria

• Chat itinerary generation creates DB records successfully.
• New trip appears in trips list after generation.
• Each day and activity is stored and linked correctly to the trip.
• On write failure, API returns clear error and rolls back partial writes.
• Tests cover successful persistence and failure behavior.

Dependencies

• Enables: frontend data wiring issue.

Out of Scope

• Redis session durability
• Observability/rate-limiting hardening