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/main.tsx

@@ -1,5 +1,6 @@
 import { render } from 'preact';
 import { initApi, fetchInit } from './api';
+import { loadTurnstile } from './captcha';
 import { Widget } from './widget';
 import type { WidgetConfig } from './types';
 
@@ -20,10 +21,19 @@ const init = async () => {
         return;
     }
 
+    // Preload Turnstile script so the captcha gate renders quickly on first open.
+    // No-op if siteKey is empty (dev mode — backend fails open).
+    if (config.captchaSiteKey) {
+        loadTurnstile().catch(() => {
+            console.warn('[HelixWidget] Turnstile preload failed — gate will retry on open');
+        });
+    }
+
     // Create shadow DOM host
+    // No font-family here — we want the widget to inherit from the host page.
     const host = document.createElement('div');
     host.id = 'helix-widget-host';
-    host.style.cssText = 'position:fixed;bottom:20px;right:20px;z-index:999999;font-family:-apple-system,sans-serif;';
+    host.style.cssText = 'position:fixed;bottom:20px;right:20px;z-index:999999;';
     document.body.appendChild(host);
 
     const shadow = host.attachShadow({ mode: 'open' });