I was struggling with a similar problem. In my scenario I was using a sandbox Mailgun account. This type of account is meant for developing purposes on a localhost environment.
But this gives it the limitation that it will only allow white-listed e-mail adresses. In the admin panel for sending the test e-mails I have configured it to use my own e-mailadres instead of the default no-reply@strapi.io e-mailadres. I was not aware that this is not sufficient of a configuration for making the forgot-password flow work. I had to go to USERS & PERMISSIONS PLUGIN > Email templates > Reset password and update the Shipper email to make sure that my forgot-password e-mails were being received in my inbox.