Move debugging variable into useEffect (vercel#50210)

## What?

Ensures the debugging variables are only assigned when the values
change.

<!-- Thanks for opening a PR! Your contribution is much appreciated.
To make sure your PR is handled as smoothly as possible we request that
you follow the checklist sections below.
Choose the right checklist for the change(s) that you're making:

## For Contributors

### Improving Documentation or adding/fixing Examples

- The "examples guidelines" are followed from our contributing doc
https://github.com/vercel/next.js/blob/canary/contributing/examples/adding-examples.md
- Make sure the linting passes by running `pnpm build && pnpm lint`. See
https://github.com/vercel/next.js/blob/canary/contributing/repository/linting.md

### Fixing a bug

- Related issues linked using `fixes #number`
- Tests added. See:
https://github.com/vercel/next.js/blob/canary/contributing/core/testing.md#writing-tests-for-nextjs
- Errors have a helpful link attached, see
https://github.com/vercel/next.js/blob/canary/contributing.md

### Adding a feature

- Implements an existing feature request or RFC. Make sure the feature
request has been accepted for implementation before opening a PR. (A
discussion must be opened, see
https://github.com/vercel/next.js/discussions/new?category=ideas)
- Related issues/discussions are linked using `fixes #number`
- e2e tests added
(https://github.com/vercel/next.js/blob/canary/contributing/core/testing.md#writing-tests-for-nextjs
- Documentation added
- Telemetry added. In case of a feature if it's used or not.
- Errors have a helpful link attached, see
https://github.com/vercel/next.js/blob/canary/contributing.md



## For Maintainers

- Minimal description (aim for explaining to someone not on the team to
understand the PR)
- When linking to a Slack thread, you might want to share details of the
conclusion
- Link both the Linear (Fixes NEXT-xxx) and the GitHub issues
- Add review comments if necessary to explain to the reviewer the logic
behind a change

### What?

### Why?

### How?

Closes NEXT-
Fixes #

-->

packages/next/src/client/components/app-router.tsx

@@ -331,17 +331,24 @@ function Router({
     return routerInstance
   }, [dispatch, navigate])
 
-  // Add `window.nd` for debugging purposes.
-  // This is not meant for use in applications as concurrent rendering will affect the cache/tree/router.
-  if (typeof window !== 'undefined') {
+  useEffect(() => {
+    // Exists for debugging purposes. Don't use in application code.
+    if (window.next) {
+      window.next.router = appRouter
+    }
+  }, [appRouter])
+
+  useEffect(() => {
+    // Add `window.nd` for debugging purposes.
+    // This is not meant for use in applications as concurrent rendering will affect the cache/tree/router.
     // @ts-ignore this is for debugging
     window.nd = {
       router: appRouter,
       cache,
       prefetchCache,
       tree,
     }
-  }
+  }, [appRouter, cache, prefetchCache, tree])
 
   // When mpaNavigation flag is set do a hard navigation to the new url.
   // Infinitely suspend because we don't actually want to rerender any child