Static page cannot load the user info starting from version 2.6.38

[Chenalejandro]

Steps to reproduce:

1. clone repo https://github.com/Chenalejandro/stackbug
2. pnpm dev
3. go to localhost:3000, click sign in and then enter the credentials to sign in

Expected: redirected back to the root page, where the user button will be shown
Actual: redirect back to the root page, but the sign in button is still there

If we go to localhost:3000/nonstaticpage, we can see the user button because it is a dynamic page. The root page is static.

You can downgrade @stackframe/stack to 2.6.37 and confirm that you can see the user button even in a static page.

This bug happens in both dev and production.

I cannot make the page.tsx a client component (with "use client";) since my component is an async function that fetches some data and statically generate the page with that data.