Migrate off of deprecated GitHub Actions save-state command

[joshlf]

In the Rust Cache step of this job, we got the following warning:

Warning: The `save-state` command is deprecated and will be disabled soon. Please upgrade to using Environment Files. For more information see: https://github.blog/changelog/2022-10-11-github-actions-deprecating-save-state-and-set-output-commands/

It seems like the warning is being generated by https://github.com/Swatinem/rust-cache, although I'm not positive. We should figure out where the warning is coming from; if it's something we can fix on our side, we should do it. If it's something that will need to be fixed in rust-cache, we should at least file an issue there.

[joshlf]

cc @AntoniosBarotsis in case you're interested

[AntoniosBarotsis]

It looks like its indeed used here.

Interestingly enough, the core library seems to account for that (rust-cache is using the latest version, 1.10) so I'm not entirely sure why the warning even happens.

The PR mentions

In the case that these commands are being used on a runner that doesn't support the file-command versions they will fallback to the pre-existing workflow commands.

Not too sure what this means though.

[joshlf]

It looks like this was fixed in #241. In particular, these PR checks (run before #241 was merged) contain the save-state warnings, but the checks for #241 itself do not.