Enable next.js version checker in turbopack (#61034)
### What
We've had the Next.js version checker in dev overlay of webpack mode.
But it was missing for turbopack. Add it in turbopack mode and also give
a small marker `"(turbo)"` to highlight turbopack mode.
Screenshot
<img width="576" alt="image"
src="https://github.com/vercel/next.js/assets/4800338/1bb1500c-fd92-43bd-a60a-ddc7cd63ce6f">
Closes NEXT-2196
Closes NEXT-2106
