How do I override all theme pagination throughout a site?

You can use pre_get_posts to override the posts_per_page setting

add_action( 'pre_get_posts', function ( $q )
{
    if (    $q->is_main_query() // Only target the main query
         && !$q->is_singular() // Do not target singular posts
    ) {
        $q->set( 'posts_per_page', -1 );
    }
});