Convert medical-centre landing to React + Tailwind v4 with amoCRM lead capture

Ports the single-file MedCsFiz page — the medical centre that already runs
physiotherapy and wants the existing room to earn more — to the same
architecture as the fitness and hotel landings: Vite + React 19 + TypeScript +
Tailwind v4 on the client, Express 5 for the API, zod schema shared between the
two.

The original stays in legacy/index.html as the visual reference. Its 4 MB of
inlined CSS, JS and base64 images become 12 asset files (664 KB) plus a bundle
loaded on demand; the two 1.5 MB / 750 KB device PNGs are recompressed to webp.
The page is split into 18 components with all copy moved to src/data/content.ts.

Leads reuse the fitness amoCRM integration: contact lookup by phone in every
Russian spelling, deal in the first stage of pipeline 10980758, account fields
matched automatically with the rest written to a note. Rate limit, honeypot and
a localStorage fallback so a lead survives the CRM being down. Endpoint is
/api/leads/medical-centers-existing-physio; Vite runs on 5173 and the API on
3000.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

medcenter/vite.config.ts

@@ -0,0 +1,21 @@
+import { defineConfig } from 'vite'
+import react from '@vitejs/plugin-react'
+import tailwindcss from '@tailwindcss/vite'
+
+export default defineConfig({
+  // Set VITE_BASE_PATH=/medical-centers/with-physiotherapy/ when the site is
+  // mounted on a sub-path, so asset URLs in the built HTML resolve against it.
+  base: process.env.VITE_BASE_PATH ?? '/',
+  plugins: [react(), tailwindcss()],
+  build: {
+    outDir: 'dist/client',
+    emptyOutDir: true,
+    assetsInlineLimit: 0,
+  },
+  server: {
+    port: 5173,
+    proxy: {
+      '/api': { target: 'http://localhost:3000', changeOrigin: true },
+    },
+  },
+})