Can't access the Email Builder template over Email Content lookup in Account Engagement

In order for an Email Template to be visible for selection when using an Email Content record, it must meet the following prerequisites:

1. The Related Entity Type on the Email Template must be either “None”, “Contact” or “Lead”. If any other related entity type is selected, then the Email Template would not be available for selection when creating an Email Content record.

2. The Email Template must not contain Salesforce Files. If it does, the Email Template would not be available for selection when creating an Email Content record. Check if "Contains Salesforce Files" is marked.

3. The “Made In Email Template Builder” checkbox has to be checked. This is checked automatically when you configure the Email Template using the “Edit in Builder” option.