Directus is a admin panel in itself (with ApIs ect out of the box)
NextJS is a frontend framework.
If you want to make an admin dashboard for your users i would use the combination of the 2.
Regarding search, you can always use an extension to improve the search experience.
You can also create custom extension. I would consider this easiest, because you already have the auth and all the juicy stuff already built in, and you just add some more functionality on top of it.
– asitanc