Auth with passwords + Playwright E2E tests + PostHog analytics

- bcrypt password hashing in auth (register, login, change-password)
- Login/register pages with password fields
- Profile update + OAuth placeholder endpoints
- Playwright test suite: auth, pages, API (3 test files)
- PostHog Docker analytics on :8010

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

apps/tasks/app/login/page.tsx

@@ -9,6 +9,8 @@ import { useTranslation } from "@/lib/i18n";
 
 export default function LoginPage() {
   const [email, setEmail] = useState("");
+  const [password, setPassword] = useState("");
+  const [showPassword, setShowPassword] = useState(false);
   const [loading, setLoading] = useState(false);
   const [error, setError] = useState("");
   const { setAuth } = useAuth();
@@ -24,7 +26,7 @@ export default function LoginPage() {
     setLoading(true);
     setError("");
     try {
-      const result = await login({ email: email.trim() });
+      const result = await login({ email: email.trim(), password: password || undefined });
       setAuth(result.data.token, result.data.user);
       router.push("/tasks");
     } catch (err) {
@@ -60,6 +62,28 @@ export default function LoginPage() {
               />
             </div>
 
+            <div>
+              <label className="block text-sm font-medium mb-1">{t("auth.password")}</label>
+              <div className="relative">
+                <input
+                  type={showPassword ? "text" : "password"}
+                  value={password}
+                  onChange={(e) => setPassword(e.target.value)}
+                  className="w-full px-3 py-2.5 border border-gray-300 dark:border-gray-600 rounded-lg bg-white dark:bg-gray-800 focus:ring-2 focus:ring-blue-500 focus:border-transparent outline-none pr-10"
+                  placeholder="******"
+                  autoComplete="current-password"
+                />
+                <button
+                  type="button"
+                  onClick={() => setShowPassword(!showPassword)}
+                  className="absolute right-3 top-1/2 -translate-y-1/2 text-gray-400 hover:text-gray-600 dark:hover:text-gray-300 text-sm"
+                  tabIndex={-1}
+                >
+                  {showPassword ? t("auth.hidePassword") : t("auth.showPassword")}
+                </button>
+              </div>
+            </div>
+
             <button
               type="submit"
               disabled={loading}
@@ -69,6 +93,12 @@ export default function LoginPage() {
             </button>
           </form>
 
+          <div className="mt-4 text-center">
+            <Link href="/forgot-password" className="text-sm text-blue-600 hover:underline">
+              {t("auth.forgotPassword")}
+            </Link>
+          </div>
+
           <p className="text-center text-sm text-muted mt-4">
             {t("auth.noAccount")}{" "}
             <Link href="/register" className="text-blue-600 hover:underline">