[CI] Stop using deprecated Actions params

[issyl0]

Verification

• This issue's title and/or description do not reference a single formula e.g. brew install wget. If they do, open an issue at https://github.com/Homebrew/homebrew-core/issues/new/choose instead.

Provide a detailed description of the proposed feature

GitHub are deprecating set-output, save-state in favour of "Environment Files".

https://github.blog/changelog/2022-10-11-github-actions-deprecating-save-state-and-set-output-commands/

What is the motivation for the feature?

Reducing noise in the "Checks" view on a PR.

How will the feature be relevant to at least 90% of Homebrew users?

It won't, but it'll reduce cognitive load for maintainers seeing these warnings.

What alternatives to the feature have been considered?

Leave them and let our Actions break in June 2023.

[Bo98]

Yeah was non-trivial work it turned out but I think most of the tricky stuff is dealt with. setup-homebrew is the big one and that's sorted. actions/cache@v3 can now be used but with care (it rarely errors if it's not working) - I can pick up that.

There's a couple of tasks in Homebrew/actions that needs sorting too.

Not sure if there's anything else. These warning overviews don't exactly tell you the relevant step/action it happened in.

[CodeWithShreyans]

@Bo98 checkout my PR, seems to fix the cache issue.