How to send image from server to client with REST API

Its just a string. Send it in your reply. Don't send the image itself.

how can I show you. I dont know how you know where the image is for this user?

So, in $user_profile->profile_picture you save the path to the user's picture as

profile-pictures/timestamp.originalname.originalextension

and the image is in the public_path (/public/profile-pictures etc etc)

so in your controller you need to return the URL to this

$url = asset($user->profile_picture);