openai/gpt-chat-latest → A (4:1)

Side A delivers a functional URL routing redesign by introducing shared `room_route_segment`/`room_id_from_route_segment` helpers, updating all server routes and handlers to use the new single-segment `/r/{room_key}` format, synchronizing ID generation via `ROOM_SHORT_ID_LEN`, and adding URL normalization logic (including YouTube canonicalization and query normalization) with tests. Side B is primarily an architectural refactor that centralizes existing path and URL helper types into `slug_types::paths` and replaces string helpers with typed wrappers across the API, improving organization and type safety but largely preserving behavior.