I opened a case with Salesforce and the result was that "Enhanced Email" was disabled. This is the fix:
=============== Objects not available under "Related Entity Type" in Lightning email template https://help.salesforce.com/articleView?id=000349235&language=en_US&mode=1&type=1
However, before you enable this, please review the articles below about Enhanced Email.
Learn about the 'Enhanced Email' and EmailMessage objects https://help.salesforce.com/articleView?id=000313606&type=1&mode=1
Use Enhanced Email for More Email Functionality https://help.salesforce.com/articleView?id=sf.emailadmin_enhanced_email_overview.htm&type=5
To enable enhanced email, here are the steps.
- Click the gear icon on the upper right side, then click Setup
- On the quick find box on the left, type 'Enhanced Email'
- Click 'Enable'