Hello Sam,
There is a trick to sort the posts by modified date. You can create a custom field date_picker and create an admin column to display this field value and sortable, then use the WordPress function get_the_modified_date()
to get the modified date and update this data for the field.
This is the example code:
add_action( 'save_post', function( $post_id ) {
$modified_date = get_the_modified_date( '', $post_id );
update_post_meta( $post_id, 'date_field', $modified_date );
} );
You might need to check the post type or something else on your end. Please read more on the documentation
https://developer.wordpress.org/reference/functions/get_the_modified_date/
https://docs.metabox.io/extensions/mb-admin-columns/#3-advanced-configuration