What's the preprocess function for targeting the home page in a Drupal 8 site? Can I use a preprocess function that is called only for the home page?
What you call home page, for Drupal is the front page. The suggestion given by
system_theme_suggestions_page(), an implementation of
hook_theme_suggestion_HOOK() from the System module, is page__front; similarly,
system_theme_suggestions_html() suggests html__front. Both the suggestions are for the preprocess functions and the template files.
If by home page you mean a page that is not the front page, you need to write your own
hook_theme_suggestions_HOOK() implementation that gives the right suggestion for that page. Keep in mind that the suggested template file is used only if it exists; otherwise, Drupal will use a different suggestion, or the default template file, if none of the suggested template files exist.