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/src/components/SignUp.tsx

@@ -0,0 +1,42 @@
+import { useState, type FormEvent } from 'react';
+
+type SignUpProps = {
+  onSignUp: (email: string, password: string) => Promise<void>;
+};
+
+export function SignUp({ onSignUp }: SignUpProps) {
+  const [email, setEmail] = useState('');
+  const [password, setPassword] = useState('');
+  const [error, setError] = useState<string | null>(null);
+  const [submitting, setSubmitting] = useState(false);
+
+  async function submit(event: FormEvent) {
+    event.preventDefault();
+    setError(null);
+    setSubmitting(true);
+    try {
+      await onSignUp(email, password);
+    } catch (err) {
+      setError(err instanceof Error ? err.message : 'Something went wrong');
+    } finally {
+      setSubmitting(false);
+    }
+  }
+
+  return (
+    <form className="wursor-signup" onSubmit={submit}>
+      <input name="email" type="email" aria-label="Email" value={email} onChange={(e) => setEmail(e.target.value)} />
+      <input
+        name="password"
+        type="password"
+        aria-label="Password"
+        value={password}
+        onChange={(e) => setPassword(e.target.value)}
+      />
+      {error ? <p role="alert">{error}</p> : null}
+      <button type="submit" disabled={submitting}>
+        Sign up
+      </button>
+    </form>
+  );
+}