Add live profile playtest and input fixes

tests/test_profile_playtest_js.py

@@ -0,0 +1,16 @@
+from __future__ import annotations
+
+import shutil
+import subprocess
+from pathlib import Path
+
+
+def test_profile_playtest_math() -> None:
+    root = Path(__file__).resolve().parents[1]
+    node = shutil.which("node")
+    assert node is not None, "Node.js is required for Profile Studio tests"
+    _ = subprocess.run(
+        [node, str(root / "tests" / "profile_playtest_test.js")],
+        check=True,
+        cwd=root,
+    )