Though I don't use Employee Engagement, it might be that you are sending the Preview link to the user and the Preview link's Share setting is set to "Brand internal only". Try changing this setting to "Public".
"All new and existing surveys will have their preview links limited to Brand internal only by default. If the preview link is shared, users will be prompted to login to their Qualtrics account and will only be able to access the preview once they have successfully logged in."
If you are using the ‘send test email’ function through the Messages tab, it’s easy to miss but on that window there is a note that it will not include project links or piped text, so it’s not a great way to check that those pieces are working. It’s more to determine deliverability and what the message looks like.
I generally like to send a live email to myself after adding my user to the participant list, that way I can ensure deliverability, piped text functionality, and that the survey links takes me to the appropriate survey.