You’re confusing “post type support” – which means enabling “feature” (and therefore MetaBoxes) for a post – with templating.
- Go into your theme, search for the
search.php
template in the folder. - Add a Child Theme
- Add a file named
search.php
to your Child theme and copy/paste the content of your parent themes template file in there. - Exchange
the_content()
withthe_excerpt()
Keep in mind that this can highly differ from theme to theme. Some themes use “Template Parts” to add parts to build a template. Others use “Conditional Tags” to switch between parts in their code in fallback template files of the “Template Hierarchy” and others use filters or hooks to alter the output in a template.
Note: This answer is meant as a guide, not a copy/paste solution as the solution can highly differ from theme to theme.