When doing a page preprocess, how do you know if the page is a form?
Since I wanted to apply a change to the page.html.twig template based on if it was a form, I looked first for the form suggestions I was given. Since I couldn't find a way to generically apply a template to all forms, I instead created a template that I would then tell all of the forms that I have to use this template. I used a hook_theme_suggestions_HOOK_alter to add my new template and check the existing suggestions to see if the forms I want to use are part of the current suggestions:
function listed_theme_suggestions_page_alter(array &amp;$suggestions, array $variables) {
  $forms = [
    'page__user__register',
    'page__admin__people',
  ];
  foreach ($forms as $form) {
    if (in_array($form, $suggestions)) {
      $suggestions[] = 'page__forms';
    }
  }
}

From here, I can add additional forms as they are needed to use this single template. So, this solution doesn't exactly answer my original question, but it solves my original problem.