Add login gate, calculation history, and AI markdown download.

Co-authored-by: Cursor <cursoragent@cursor.com>

app/api/auth/me/route.ts

@@ -0,0 +1,19 @@
+import { NextResponse } from "next/server";
+import { cookies } from "next/headers";
+import { isAuthEnabled } from "@/lib/auth/config";
+import { getSessionUsername, SESSION_COOKIE } from "@/lib/auth/session";
+
+export async function GET() {
+  if (!isAuthEnabled()) {
+    return NextResponse.json({ authEnabled: false, loggedIn: true });
+  }
+
+  const token = (await cookies()).get(SESSION_COOKIE)?.value;
+  const username = await getSessionUsername(token);
+
+  return NextResponse.json({
+    authEnabled: true,
+    loggedIn: !!username,
+    username: username ?? undefined,
+  });
+}