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/vite.config.ts

@@ -0,0 +1,15 @@
+import react from '@vitejs/plugin-react';
+import { defineConfig } from 'vitest/config';
+
+export default defineConfig({
+  plugins: [react()],
+  server: {
+    proxy: {
+      '/auth': 'http://localhost:3000',
+    },
+  },
+  test: {
+    environment: 'jsdom',
+    setupFiles: ['./src/test-setup.ts'],
+  },
+});