- Make copying to `*_names.before.txt` the responsibility of `update.sh`
(unless the file doesn't exist at all). This provides the added
benefit of allowing the inspection of the before/after state after
running a `brew update` rather than both files always being identical
at this point.
- State `No changes to formulae or casks.` on macOS.
- Rename and flip `updated_formula_report` to `auto_update`; this naming
was confusing every time.
- Only display the `You can upgrade with...` messaging if we're not
auto-updating as sometimes it will be displayed before the commands it
references (e.g. `upgrade`, `outdated` or an `install` that proceeds
to upgrade these formulae).
Fixes https://github.com/Homebrew/brew/issues/15065
