Not a generic package manager, but it's probably worth calling out asdf as the generic version manager[0] (maybe you're already aware of it, but it's a generic replacement for nvm, rvm, virtualenv, *vm, which supports any language based on plugins.)
Again, maybe you're already aware of it, but I think it's a nice example of genericising a concern common to many languages which sounds similar to what you're asking for (albeit unfortunately in a slightly different space).
At a minimum it's useful having the `.tool-versions` dotfile in a project directory which lists the versions of each language, db, and package manager version (our Rails project lists versions for ruby, bundler, postgres, node, yarn, redis). Even if all devs don't use asdf, it's a useful reference point.
Again, maybe you're already aware of it, but I think it's a nice example of genericising a concern common to many languages which sounds similar to what you're asking for (albeit unfortunately in a slightly different space).
[0] https://github.com/asdf-vm/asdf