Hello @plewar,
It seems that your website is not able to send emails, I have tried to register from the standard wp-login.php?action=register and the email is not being received also.
You could look to contact your hosting provider about this or look to use a plugin which can override the settings coming from your webhost.
Regards.
Be sure to look in your email target’s SPAM or Junk folders. It’s common for them to be silently reassigned there.
Also, look at your website logs (where they are probably depends on your hosting provider) to see whether your emails are getting rejected.
We had problems a while back with certain email targets rejecting emails from our website — in particular, @comcast.net and @aol.com . It’s been a while, but I believe I had to set up DMARC, to allow the receiving email provider to be able to verify that your email was indeed from the domain it was claiming to be in. See, for example, https://wpengine.com/support/dmarc-best-practices-get-email-inbox/
