Emails not received and not in logs, only test emails logged and recieved

I have WP SMTP and I set it up on a test site the same way as two of my working and live websites. However, for some reason, the emails on my test site are not received and also not logged by email loggers. I am using Check and Log Email. When I use either of them to send test emails to myself, that gets logged and the emails are received. But when a test user signs up or requests a password change, it is not received nor logged.

Just to be clear, by test site I meana site that I am using to conduct tests on. It is a live site with its own domain URL and hosting account, not a staging account.

The only thing I can think of is it currently does not have an SSL apparently, even though my hosting account admin page says there is and is active. Sometimes when I try to access the site when logged out, I get a “Your clock is ahead” message and won’t let me access it (even though the device clock is not ahead). Maybe it’s the SSL or clock error that stops the emails being sent?