feat(logging): implement structured logging backend with SQLite persistence and logs API

[cto-new]

Summary

Introduce a fully functional logging backend: SQLite-backed log repository, CoreService integration, and a server-side logs API.

Details

• Add log_repository.py implementing SQLite storage, query/export, and pruning
• Extend CoreService to persist logs, add log helpers (log_transfer/log_share/log_recursive) and notify listeners
• Wire up logs API: /api/logs/query, /api/logs/export, /api/logs/stats, /api/logs/clear, /api/logs/prune with filter, pagination, tail support and export options
• Add tests: tests/test_logging_backend.py and tests/test_logs_api.py for insertion, filtering, pagination, tail mode, and export serialization
• Update docs: create LOGGING_API.md and reference it from WEBUI_GUIDE; update .gitignore to exclude ephemeral logs
• Demonstrate via curl examples