There could be a lot of reasons why email notifications don't work. But first, check the Settings. Check the Default appointment status of newly booked appointments in Settings > General tab.
In case you’re using the built-in cart and want to send one notification for all the time slots from the cart, you need to enable combined notifications with relevant status in Email Notifications tab in Bookly menu.
The combined notifications will only be sent when customers book an appointment on the front-end. When you manually add an appointment in the back-end single notifications are being sent.
Access Email Notifications tab in Bookly menu and make sure that both types of email notifications are enabled (Single and Combined).
For example, if the default status is "Approved" and combined notifications are disabled, then you need to enable "Notification to customer about approved appointment".
Another point to check is Sender email address. A lot of hosting providers have a restriction and don’t allow sending notifications from another domain. For example, your domain name is www.example.com and you set firstname.lastname@example.org as a Sender email address. Your email notifications might not be sent because your hosting provider allows to send them only from email@example.com.
Besides, you can also check if the problem is with Bookly or not with the "Test email notifications" tool. In case you don't receive email notifications then it means that your website doesn't send email notifications at all and you need to contact your hosting provider.
In some cases, the problem relates to your server configuration when emails are marked as spam and are blocked by some email servers. To troubleshoot this issue, try to install a 3rd party plugin – WP Mail Logging – that logs each email sent by WordPress. Then make a new appointment and check the mail log. If you find there all the Bookly email notifications, then the problem is not on the Bookly side. It may be happening because of problems in your mail server. Bookly uses native WP function - wp_mail(). If you install any SMTP plugin and configure it, the problem should be solved. For example, you can use Easy WP SMTP for the test. You can ask your hosting provider about SMTP settings. See this link for more details regarding this issue.
If the issue persists after you’ve adjusted all the settings, please contact us at firstname.lastname@example.org, so we could look into this matter.