1 . Please first check if youe forget password email is going from wp-login.php page ?
Install and configure WP Mail SMTP plugin also checks touch-points in lms setting.
tip: https://wplms.io/support/knowledge-base/postman-smtp-for-emails/
Please check Another type of emails such as 'WP Mail SMTP test email', 'WooCommerce order emails' and 'manual user registration via WordPress settings' are working or not??
***if you are receiving other emails and not only registration activation then
please try adding this given code in your wplms-customizer.php file in wplms customizer plugin :
add_filter( 'bp_email_use_wp_mail', '__return_true' );
Sometimes the problem is, it is going in the spam folder because some hosting providers block the WordPress default mail and keep them as spam. so please check your spam folder.
2 . this is strange we are using wordpress core function " wp_logout_url " there .
Please share your site url and admin credentials to check this . Try deactivating third party plguins in your site .