How to split the long task that straddles `_app.tsx` and `pages/index.tsx` in Nextjs?

I use NextJS and try to improve the performance along the CoreWebVitals. I would like to split the long task that straddles _app.tsx and pages/index.tsx.

In the image above, the tree on the left is for _app.tsx and the tree on the right is for pages/index.tsx. I can simply run it asynchronously, but I don't know how to do it with NextJS.

Is there any good way?