feat: finish Better Auth config

app/routes/api.auth.$.ts

@@ -0,0 +1,10 @@
+import { auth } from "../../lib/auth";
+import type { LoaderFunctionArgs, ActionFunctionArgs } from "react-router";
+
+export async function loader({ request }: LoaderFunctionArgs) {
+  return auth.handler(request);
+}
+
+export async function action({ request }: ActionFunctionArgs) {
+  return auth.handler(request);
+}