Please install the following plugin: https://wordpress.org/plugins/log-emails/
Then make test registration.
After navigate to Dashboard – Tools – Email Log and check if registration email was sent by WordPress.
If yes, but nothing is in your Inbox – then probably you should configure SMTP on your website: https://wordpress.org/plugins/wp-mail-smtp/
There are no records in Dashboard – Tools – Email Log
And woocommerce emails are sent without problems
And you didn’t get any errors?