hook or similiar to automatically send any webform submissions to an email address, without manually adding a handler to each existing webform?
I am going to go ahead and say No, there isn't any hook or otherwise automated way to do this.

I looked at hook_entity_insert(), as leymaxx suggested. From looking at the Webform Submission entity at /src/Entity/WebformSubmission.php, it appeared to me that the Webform Submission entity is not what triggers the emails and handlers of the webform, but rather the Webform entity does.

Looking further at the Webform entity at /src/Entity/WebformSubmission.php, I found functions for invoking handlers, but these only appeared to loop through existing handlers already attached to the Webform entity. So, there is no way to call an arbitrary handler on a webform. 

What I'm going to do is create a custom handler, attach it manually to existing webforms, and use this recipe that I referenced in my question to have it automatically attached to new webforms as they are created.

Edit We are using config_export on our site, which has yamls for all of our current webforms. Because of this, I was able to copy and paste the additional email handler into the yaml, and do a config import, to update existing webforms. This saved some time over manually editing them in the web interface.