Has the situation changed at all in the seven years since? I am personally most interested in being able to install user-facing documentation for command line tools -- including but not necessarily limited to manpages -- but existing general-purpose build systems have a whole taxonomy of things you might want to install and where they should go.
Note that installing things such as manpages generally should be done as part of a package fed to the system's package manager, so that their provenance can be tracked and they can be removed when no longer wanted. So, you can look at tools for packaging Rust programs, and let the package manager take care of the "installation" per se.