Hi partner,
You could create a workflow triggered when creating emails from contact, here are the steps.
1.Create a new workflow based on email and set the trigger condition to when creating a new record.

2.Add another condition as if Regarding(Contact) fullname contains data, so that we could know if this emails is created from contact.

3.Add an updating action and configure the email body.


4.Then I created an email from contact timeline, and after save it, the link will be filled in automatically.

Hope it helps.
Best regards,
Leo