wp-includes/functions.php is never a file you should modify. Any mention of adding something to functions.php is never referring to this file.
Functions related to front-end display or theme behavior should go in your theme’s functions.php. If the theme may potentially be updated, then you should be using a Child Theme to add functionality, and they should go in your child theme’s functions.php. Child themes are update-safe – a core update will not overwrite a child theme.
For any code that should persist regardless of active theme, those functions should go in your own plugin. Your own plugins are update-safe.
Regardless of what option you choose, you should always have a local recent backup in case you need to restore things.