Show New/Deleted Formulae/Casks from brew update

[MikeMcQuaid]

If we're installing from the API: we cannot use Git to check for differences in
packages so instead use {formula,cask}_names.txt to do so.

The first time this runs: we won't yet have a base state
({formula,cask}_names.before.txt) to compare against so we don't output
anything and just copy the files for next time.

Fixes #14706

[BrewTestBot]

Review period will end on 2023-02-27 at 17:30:54 UTC.

[Bo98]

Idea here makes sense, yeah. 👍

[apainintheneck]

This general approach makes sense to me.

[BrewTestBot]

Review period ended.

[MikeMcQuaid]

This is now ready for review/testing.

Note: because this is only changing the update-report.rb part: if we break something, we can push updates and the latest version on master (or a tag) will be used after the update.sh Bash side updates things.

[apainintheneck]

What would be the best way to test this? I checked this branch out yesterday and ran brew update and then just did the same thing again right now but it looks like no new casks/formulae have been added in that time.

[MikeMcQuaid]

I'm confident enough in this to merge as-is. Should probably follow-up letting people with HOMEBREW_UPDATE_REPORT_ALL_FORMULAE set that it won't work while using the API (therefore probably worth deprecating this setting).

Feel free to revert if this seems to introduce problems.

[RandomDSdevel]

Should probably follow-up letting people with HOMEBREW_UPDATE_REPORT_ALL_FORMULAE set that it won't work while using the API (therefore probably worth deprecating this setting).

     No, just do only the former. Folks who set 'HOMEBREW_NO_INSTALL_FROM_API' who've also set 'HOMEBREW_UPDATE_REPORT_ALL_FORMULAE' will still want the latter's behavior.

(Edit: Never mind, I see that this is already what #14866 does; feel free to ignore my comment here.)