I would start by enumerating the directories in ~/.cargo and which ones you think would be appropriate to treat as cache directories. Then submit that list as an issue on the cargo repository for review. (Also feel free to ping #t-cargo on Zulip once you've filed that issue.) Once that list gets reviewed, then a PR would be appropriate.
That way, we don't iterate on the list of directories in the PR.
Which essential files does the folder even contain? I have set export $CARGO_HOME=$XDG_CACHE_HOME/cargo years ago and not noticed any issues. Therefore wouldn't it suffice to simply put the CACHEDIR.TAG on the top level?
~/.cargo/bin/ contains every binary installed by cargo install. In theory perhaps they can all be recreated, but not trivially: they might have come from local trees, or now-pulled crates. I think it's reasonable to back them up: the user might care to get back the same version.
Maybe eventually those binaries should move to a different directory, or be left behind if the rest moves into ~/.cache.
~/.cargo/config, ~/.cargo/credentials contain small amount of user config that should be backed up.