livecheck: update --newer-only and --quiet behavior

[samford]

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It was mentioned in #13395 that skip messages are printed when livecheck's --newer-only option is used and there's currently no way to avoid this. That issue suggested an --ignore-skipped option but we agreed that it's simpler to update livecheck's behavior to omit skip messages when the --newer-only option is used. [If a user also wants to omit error messages (i.e., only printing newer formulae/casks), they can use --newer-only --quiet.]

This PR implements the aforementioned change and also brings the JSON output in line by making the --newer-only and --quiet options apply to --json runs. This gives users a bit of control over the JSON output without having to manually filter it themselves.

Resolves #13395.

[BrewTestBot]

Review period will end on 2022-06-09 at 20:09:50 UTC.

[MikeMcQuaid]

Makes sense to me, thanks!

[BrewTestBot]

Review period skipped due to critical label.