Added support for query params on not found pages (#43836)

Previously, query parameters were not available on 404 pages because
calling the router methods would change the pathname in the browser.
This change adds support for the query to update for those pages without
updating the path to include the basePath.

This additionally narrows some Typescript types that were previous set
to `any` which highlighted some type errors that were corrected.

Fixes: #35990

Co-authored-by: JJ Kasper <jj@jjsweb.site>

packages/next/client/index.tsx

@@ -116,11 +116,6 @@ class Container extends React.Component<{
     // - if rewrites in next.config.js match (may have rewrite params)
     if (
       router.isSsr &&
-      // We don't update for 404 requests as this can modify
-      // the asPath unexpectedly e.g. adding basePath when
-      // it wasn't originally present
-      initialData.page !== '/404' &&
-      initialData.page !== '/_error' &&
       (initialData.isFallback ||
         (initialData.nextExport &&
           (isDynamicRoute(router.pathname) ||