The hashicorp/vault image is presumably built from this Dockerfile. But that Dockerfile just copies the binary in - it has to be already built. Is it built with make ci-build-ui? Could we know the exact flags so that we can recreate it locally?
I suggest that you probably have a better chance of a resolution to this, if you log a GitHub issue asking that this be documented.
The reason is, GitHub issues have an open/closed state, and are usually used for things which actually require resolution on the Vault side, whereas discussion topics rapidly fade into being ignored after a few days inactivity, and are usually used for advice or recommendations which don’t require any resolution within the Vault project itself.