It is unfortunately seeming that in the Gutenberg editor there is not yet a way to keep subscribers from seeing specific posts using a code snippet or plug-in. That said, this post is evidence that if I publish it privately subscribers will not be notified. This could be a solution, but I am going to try a change it to public and see what happens… Nope, never mind. The notification goes out when we change the status to public.
I also tried the plug-in “Notification,” but it only lets you customize alert content by the looks of it (though there is a premium version that might have more options).
I found the same for “Publish Press.”