[docs-infra][docs] Custom 404 page for docs doesn't work since v1.0.0

## Reproducible example

1. Open https://base-ui.com/drgdrgdr
2. Open https://base-ui.com/react/overview/quick-startseff

## Current behavior

1. Default Next.js 404 error template
2. Default Next.js 404 error template

## Expected behavior

1. Custom 404 error template that match **website** layout
2. Custom 404 error template that match **docs** layout

## Base UI version

v1.0.0

## Additional context

This is a regression introduced in #3493. For example, v1.0.0-rc.2 works https://693aa73c0eca2100084ef620--base-ui.netlify.app/:

There is the same issue on Material UI's side https://github.com/mui/material-ui/issues/41042. The value is that in the case of a link break, you can quickly recover from it: 1. you know where you are, 2. you don't have to go back to the homepage, and navigate your way back to the right layout, then to the right page.

It seems to be a limitation of Next.js. I see 3 issues about the same thing, it seems:

- https://github.com/vercel/next.js/issues/59180
- https://github.com/vercel/next.js/issues/54980
- https://github.com/vercel/next.js/issues/55191