feat: bootstrap vela UI and gateway workspace

Establish the monorepo, tooling, and starter apps so UI and gateway development can begin from a documented, runnable baseline.

docs/protocol.md

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+# Vela Protocol and State Machine
+
+## Event Protocol
+
+### Client → Server
+
+```ts
+type ClientEvent =
+  | { type: "start_listening" }
+  | { type: "stop_listening" }
+  | { type: "audio_chunk"; data: string } // PCM16 base64
+  | { type: "interrupt" };
+```
+
+### Server → Client
+
+```ts
+type ServerEvent =
+  | { type: "state"; value: "idle" | "listening" | "thinking" | "speaking" }
+  | { type: "partial_transcript"; text: string }
+  | { type: "final_transcript"; text: string }
+  | { type: "assistant_text_delta"; text: string }
+  | { type: "tool_call_started"; tool: string }
+  | { type: "tool_call_finished"; tool: string; result: unknown }
+  | { type: "tts_audio_chunk"; data: string }
+  | { type: "assistant_done" }
+  | { type: "error"; message: string };
+```
+
+## State Machine
+
+```text
+idle
+ → listening
+ → thinking
+ → speaking
+ → idle
+```
+
+Interrupt can occur at:
+
+- listening → restart
+- thinking → cancel
+- speaking → stop immediately
+
+## Interrupt Handling Requirements
+
+- immediate stop of TTS playback
+- immediate stop of LLM streaming
+- reset session state to listening or idle, depending on UX decision
+
+### Mechanism
+
+The `interrupt` event cancels:
+
+- TTS process
+- current LLM request
+- tool execution when possible
+
+## Protocol Notes for Implementation
+
+- keep the protocol backward compatible when possible
+- prefer additive event changes over breaking renames
+- document protocol updates in this file whenever implementation changes behavior
+- when implementation diverges from the initial contract, update this document in the same change