1. Can your site send emails?
There could be a lot of reasons why email notifications don't work. First, check if your site can send emails at all. Bookly doesn’t send emails independently, it uses the native WordPress function wp_mail() to send all email notifications. This function sends any email messages in the entire site, not only Bookly.
To check it, install any mail checking plugin and send a test email to yourself. For example, you can use this one https://wordpress.org/plugins/check-email/
If you didn’t receive the test email please contact your hosting provider to fix this issue. Also, you can try to solve the issue yourself, installing any SMTP plugin and configure it to any mail server (SMTP is a push protocol and is used to send the mail). Here is an example how to configure SMTP to Gmail https://www.wpbeginner.com/plugins/how-to-send-email-in-wordpress-using-the-gmail-smtp-server/
2. Does Bookly send email notifications?
In some situations your site is able to send simple emails but can’t send a large email with HTML such as Bookly email notifications.
Install any mail logging plugin, make a test appointment and check the mail log. If you see that the emails are sent but they aren’t delivered, then the problem is still with your site and you should contact your hosting provider to fix this issue.
You can try this mail logging plugin https://wordpress.org/plugins/wp-mail-logging/
If there are no sent messages in the mail log, go to the next step.
3. Check Bookly email notifications.
Check the Default appointment status of newly booked appointments in Settings > General tab.
In case you’re using the Bookly Cart (Add-on) 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 section 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 section 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 email@example.com as a Sender email address. Your email notifications might not be sent because your hosting provider allows to send them only from firstname.lastname@example.org.