feat(chat): unify session gateway with stable IDs and a single WS protocol

The frontend previously juggled placeholder IDs, provider-native IDs, and session_created handoffs, which caused race conditions and provider-specific branching. This introduces app-allocated session IDs, a chat run registry with event replay, delta sidebar updates, and one kind-based websocket contract so the UI can treat every provider the same while JSONL remains the source of truth.