I do this with Nix. You just tell it what applications to put into the image and it will copy just the image and its dependencies.

https://gitlab.com/kevincox/feed-test/-/blob/1a09590e98608ed...

This is a trivial example but even that will pull in libc and some TZ data if required. I've also used this to package up more complex dependencies with data files and lots of native libraries such as the mumble server.