Find most popular images with `zip` and `git` on Docker Hub
I can answer half of your question: If you have a set of images you're trying to investigate, the best way would be to use which in a new container using the image in question. This way you can quickly see if a particular image has the binaries your are looking for already on PATH:

docker run --rm ubuntu:latest which zip git
# no result

docker run --rm ubuntu:latest which bash sh
/bin/bash
/bin/sh
# ^-- both bash and sh are in the image


I don't know of a way to discover the set of images in question, as there is no manifest of files that a registry will provide. That is, yes, an image is a set of tar files, which you can extract a set of files/directory names... however, you'd still need to pull the entire image to get this information, so it would be easier to run the which command above.

There are tools for exploring information that a registry exposes (skopeo, doocker-ls, reg, manifest-tool, etc) but none of them will do exactly what you're looking for, which is "find a repository within a registry which contains an image that has a particular binary in it".