Hi Erin,
Thanks for using Microsoft products and posting in the community, I'm glad to offer help.
According to your description, it seems that you want to add "mailto: links so that user can open a mail app to send a new email to the specific address directly when clicking the link.
In this case, you can follow the steps below to add "mailto:" links to Text web part:
1. Open and Edit the page.
2. Add a Text webpart.
3. Press Ctrl + K to add a new hyperlink.
4. Type "mailto:adress" in Address and display text in "Text to play".
Reference: How to add a mailto link or button to modern sharepoint page
Besides, I noticed that you want to add "mailto:" links to a People web part, so I also tested on my side, however as you've know, I'm afraid I have to say that it is unavailable for People web part.
Hope the above information can be helpful, and please feel free to let me know if there is any progress or you have any concerns, I'll continue to help you.
Best Regards,
Arck