feat: Sprint 1 slice 1 — API signup + web signup/chat shell

- api: Fastify POST /auth/signup (validation, scrypt hash, in-memory store)
- web: React+Vite SignUp form and chat shell with dev proxy
- 35 tests green (api 5, web 2, e2e 28)

web/package.json

@@ -2,5 +2,26 @@
   "name": "@wursor/web",
   "private": true,
   "type": "module",
-  "scripts": {}
+  "scripts": {
+    "test": "vitest run",
+    "dev": "vite",
+    "build": "tsc -b && vite build",
+    "preview": "vite preview"
+  },
+  "dependencies": {
+    "react": "^19.2.8",
+    "react-dom": "^19.2.8"
+  },
+  "devDependencies": {
+    "@testing-library/jest-dom": "^7.0.1",
+    "@testing-library/react": "^16.3.2",
+    "@testing-library/user-event": "^14.6.4",
+    "@types/react": "^19.2.18",
+    "@types/react-dom": "^19.2.4",
+    "@vitejs/plugin-react": "^6.0.5",
+    "jsdom": "^30.0.1",
+    "typescript": "^5.9.3",
+    "vite": "^8.2.1",
+    "vitest": "^3.2.7"
+  }
 }