feat(gateway): add WebSocket gateway with JSON-RPC protocol and auth

Phase 2 of the Flynn roadmap. Adds a WebSocket gateway server that
starts alongside the Telegram bot, providing real-time API access to
the agent, sessions, and tools.

Protocol: JSON-RPC-like (request/response/event) over WebSocket.
8 methods: agent.send, agent.cancel, sessions.list, sessions.history,
sessions.create, tools.list, tools.invoke, system.health.

Auth: Bearer token + Tailscale identity header support.
Session bridge: per-connection agent instances with shared model router.

New files: src/gateway/ (protocol, router, server, auth, session-bridge,
handlers for agent/sessions/tools/system).
57 new tests (181 total), typecheck clean.

src/gateway/session-bridge.test.ts

@@ -0,0 +1,144 @@
+import { describe, it, expect, vi, beforeEach } from 'vitest';
+import { SessionBridge } from './session-bridge.js';
+import type { SessionBridgeConfig } from './session-bridge.js';
+
+// Minimal mocks
+const mockSession = {
+  id: 'test',
+  addMessage: vi.fn(),
+  getHistory: vi.fn(() => []),
+  clear: vi.fn(),
+};
+
+const mockSessionManager = {
+  getSession: vi.fn(() => mockSession),
+  listSessions: vi.fn(() => []),
+  transferSession: vi.fn(),
+  closeSession: vi.fn(),
+};
+
+const mockModelClient = {
+  chat: vi.fn(async () => ({
+    content: 'test',
+    stopReason: 'end_turn',
+    usage: { inputTokens: 0, outputTokens: 0 },
+  })),
+};
+
+const mockToolRegistry = {
+  register: vi.fn(),
+  get: vi.fn(),
+  list: vi.fn(() => []),
+  toAnthropicFormat: vi.fn(() => []),
+  toOpenAIFormat: vi.fn(() => []),
+};
+
+const mockToolExecutor = {
+  execute: vi.fn(),
+};
+
+function createBridge(): SessionBridge {
+  return new SessionBridge({
+    sessionManager: mockSessionManager as unknown as SessionBridgeConfig['sessionManager'],
+    modelClient: mockModelClient,
+    systemPrompt: 'test prompt',
+    toolRegistry: mockToolRegistry as unknown as SessionBridgeConfig['toolRegistry'],
+    toolExecutor: mockToolExecutor as unknown as SessionBridgeConfig['toolExecutor'],
+  });
+}
+
+describe('SessionBridge', () => {
+  beforeEach(() => {
+    vi.clearAllMocks();
+  });
+
+  it('connect assigns a connection ID', () => {
+    const bridge = createBridge();
+    const id = bridge.connect('conn-1');
+    expect(id).toBe('conn-1');
+    expect(bridge.connectionCount).toBe(1);
+  });
+
+  it('connect auto-generates ID when not provided', () => {
+    const bridge = createBridge();
+    const id = bridge.connect();
+    expect(typeof id).toBe('string');
+    expect(id.length).toBeGreaterThan(0);
+  });
+
+  it('getAgent returns agent for connected client', () => {
+    const bridge = createBridge();
+    bridge.connect('conn-1');
+    const agent = bridge.getAgent('conn-1');
+    expect(agent).toBeDefined();
+  });
+
+  it('getSessionId returns session ID for connected client', () => {
+    const bridge = createBridge();
+    bridge.connect('conn-1');
+    expect(bridge.getSessionId('conn-1')).toBe('ws:conn-1');
+  });
+
+  it('disconnect removes client but preserves session', () => {
+    const bridge = createBridge();
+    bridge.connect('conn-1');
+    bridge.disconnect('conn-1');
+    expect(bridge.connectionCount).toBe(0);
+    expect(bridge.getAgent('conn-1')).toBeUndefined();
+  });
+
+  it('tracks busy state', () => {
+    const bridge = createBridge();
+    bridge.connect('conn-1');
+    expect(bridge.isBusy('conn-1')).toBe(false);
+    bridge.setBusy('conn-1', true);
+    expect(bridge.isBusy('conn-1')).toBe(true);
+    bridge.setBusy('conn-1', false);
+    expect(bridge.isBusy('conn-1')).toBe(false);
+  });
+
+  it('switchSession changes session for a connection', () => {
+    const bridge = createBridge();
+    bridge.connect('conn-1');
+    expect(bridge.getSessionId('conn-1')).toBe('ws:conn-1');
+
+    bridge.switchSession('conn-1', 'custom-session');
+    expect(bridge.getSessionId('conn-1')).toBe('custom-session');
+  });
+
+  it('switchSession throws when busy', () => {
+    const bridge = createBridge();
+    bridge.connect('conn-1');
+    bridge.setBusy('conn-1', true);
+
+    expect(() => bridge.switchSession('conn-1', 'other')).toThrow('Cannot switch session while agent is busy');
+  });
+
+  it('switchSession throws for unknown connection', () => {
+    const bridge = createBridge();
+    expect(() => bridge.switchSession('unknown', 'other')).toThrow('Unknown connection');
+  });
+
+  it('listSessions groups connections by session', () => {
+    const bridge = createBridge();
+    bridge.connect('conn-1');
+    bridge.connect('conn-2');
+    // Switch conn-2 to share conn-1's session
+    bridge.switchSession('conn-2', 'ws:conn-1');
+
+    const sessions = bridge.listSessions();
+    expect(sessions).toEqual([{ sessionId: 'ws:conn-1', connections: 2 }]);
+  });
+
+  it('shared sessions keep agent alive when one client disconnects', () => {
+    const bridge = createBridge();
+    bridge.connect('conn-1');
+    bridge.connect('conn-2');
+    bridge.switchSession('conn-2', 'ws:conn-1');
+
+    bridge.disconnect('conn-1');
+    // conn-2 still has the session
+    expect(bridge.getAgent('conn-2')).toBeDefined();
+    expect(bridge.connectionCount).toBe(1);
+  });
+});