You can add a new bulk action for posts with this code :
$postType = "post";
add_filter("bulk_actions-edit-" . $postType, function ($actions) {
$actions["specialSave"] = "Special save";
return $actions;
}, 20);
add_filter("handle_bulk_actions-edit-" . $postType, function ($sendback, $doaction, $post_ids) {
if ("specialSave" !== $doaction) {
return;
}
foreach ($post_ids as $idPost) {
// action to do for each selected post
}
return $sendback;
}, 10, 3);
is a simple save is not enough to set the value, you can use this code to set the value directly for each selected post.