Changing the PATH changes the `tar` command used by the cache

In https://github.com/actions/cache/issues/465, the user's workflow was modifying the PATH while installing some custom software. This changed the tar implementation found when searching the PATH because it added C:/Program Files/Git/usr/bin. This broke caching since the cache action expected to use "BSD tar with GZip" during the restore step but would save the cache using "GNU tar with Zstd".

There is already work underway to always use GNU tar (when available), but even this could potentially run into issues if:

1. The user modifies the PATH env var and removes all tar implementations
2. The system starts without GNU tar but the user installs it in a subsequent step.

It therefore seems like we need the cache to "lock onto" a particular version of tar. My thinking is to record the tar implementation in the state which can then be used in the post step.

Start by locating the cache implementation that performs the restore and post steps, then read how it discovers tar and persists state between those steps. Reproduce the PATH changes described in the issue and verify that restore and save use the same tar implementation, including when tar is unavailable or installed later.