Dear Jolyn Johnson,
Good day! Thank you for posting to Microsoft Community. We are happy to help you.
As per your description, please don’t worry, we can work together to narrow down and resolve the situation.
Based on my test result, I can confirm in SharePoint online site page using the quick links web part, I'm afraid to say that it is not accepting the link (\*\*\*\*\*\*@domain.com). And It seems to be expecting a link that must start with https://
Regarding to your requirement, as a workaround, you may insert/ add a "Text" web part and insert a hyperlink with ”mailto:******@domain.com“. And when you click on email it will launch Microsoft Outlook or the email client.
Screenshot of workaround:
Your understanding and patience will be highly appreciated. I hope that you are keeping safe and well!
Sincerely,
Waqas Muhammad