Add q parameter to ListQuery with into_request_and_search(). Extend
ListNavigator with search state, search_value(), has_search(), path(),
and search_query_base() for template URL generation. Thread search
through all route handlers and update backup tests.
- Add BackupData struct and BackupService with raw SQL export/import
- Restore uses raw inserts to bypass brew deductions and timeline creation
- Restore requires an empty database, inserts in FK dependency order
- Add comprehensive e2e test verifying full round-trip fidelity