How can I confirm I’m on the home page

If you are using the default home page, which in most cases is a list of most recent posts, is_home() should work.

If you have set a static page to be your front page (in Settings >> Reading), is_front_page() should work. If you are not getting the results you expect using this:

if (is_front_page()) {
  //the code you want to execute
}

perhaps you can describe your situation in more detail.