When you use Sync & Customize on a HomeRunner template, that one template file is copied into the Template Customizer, and your copy takes over rendering for that template.
What happens on update. Plugin updates never overwrite your customized copy, so your changes are kept through every update. Your copy is a fork of that single file, but not a silent one. When a HomeRunner update changes the original template, the Template Customizer marks your copy as outdated in wp-admin so you know the original has changed.
Re-syncing. Re-syncing pulls in the new original and backs up your customized copy first. Re-applying your changes on top of the new version is a manual step.
Choosing CSS or Sync & Customize. If your changes are visual, use CSS in Appearance > Additional CSS. CSS-only changes survive every plugin update with nothing to re-apply. Use Sync & Customize only for structural changes to the page markup that CSS cannot achieve.