feat: widget chat with generative UI, branch selection, captcha gate, lead dedup

- Streaming AI chat via Vercel AI SDK v6 UI message stream — tool-based
  generative UI (pick_branch, list_departments, show_clinic_timings,
  show_doctors, show_doctor_slots, suggest_booking). Typing indicator,
  markdown suppressed, text parts hidden when widgets are rendered.
- Centralized Preact store (store.tsx) for visitor, leadId, captchaToken,
  bookingPrefill, doctors roster, branches, selectedBranch — replaces prop
  drilling across chat/book/contact tabs.
- Cloudflare Turnstile captcha gate rendered via light-DOM portal so it
  renders correctly inside the shadow DOM (Turnstile CSS doesn't cross
  shadow boundaries).
- Lead dedup helper (findOrCreateLeadByPhone, 24h phone window) shared
  across chat-start / book / contact so one visitor == one lead. Booking
  upgrades existing lead status NEW → APPOINTMENT_SET via updateLeadStatus.
- Pre-chat name+phone form captures the visitor; chat transcript logged
  to leadActivity records after each stream.
- Booking wizard gains a branch step 0 (skipped for single-branch
  hospitals); departments + doctors filtered by selectedBranch. Chat slot
  picks prefill the booking details step and lock the branch.
- Window-level captcha gate, modal maximize mode, header badge showing
  selected branch, widget font inherits from host page (fix :host { all:
  initial } override).
- 23 FA Pro 7.1 duotone icons bundled — medical departments, nav, actions,
  hospital/location-dot for branch context.
- main.ts: resolve public/ from process.cwd() so widget.js serves in both
  dev and prod. tsconfig: exclude widget-src/public/data from server tsc.
- captcha.guard: switch from reCAPTCHA v3 to Cloudflare Turnstile verify.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

widget-src/src/api.ts

@@ -47,10 +47,28 @@ export const submitLead = async (data: any): Promise<{ leadId: string }> => {
     return res.json();
 };
 
-export const streamChat = async (messages: any[], captchaToken?: string): Promise<ReadableStream> => {
+export const startChatSession = async (name: string, phone: string): Promise<{ leadId: string }> => {
+    const res = await fetch(`${baseUrl}/api/widget/chat-start?key=${widgetKey}`, {
+        method: 'POST', headers: headers(),
+        body: JSON.stringify({ name, phone }),
+    });
+    if (!res.ok) throw new Error('Chat start failed');
+    return res.json();
+};
+
+// Send the simplified {role, content: string}[] history to the backend.
+// Backend responds with an SSE stream of UIMessageChunk events.
+// branch (when set) is injected into the system prompt so the AI scopes
+// tool calls to that branch.
+type OutboundMessage = { role: 'user' | 'assistant'; content: string };
+export const streamChat = async (
+    leadId: string,
+    messages: OutboundMessage[],
+    branch: string | null,
+): Promise<ReadableStream<Uint8Array>> => {
     const res = await fetch(`${baseUrl}/api/widget/chat?key=${widgetKey}`, {
         method: 'POST', headers: headers(),
-        body: JSON.stringify({ messages, captchaToken }),
+        body: JSON.stringify({ leadId, messages, branch }),
     });
     if (!res.ok || !res.body) throw new Error('Chat failed');
     return res.body;