If someone is on the extended maternity leave, does it mean that she has delievered the baby already or not?

This is the context I have received. "I will be out of the office beginning Monday, August 1, on extended maternity leave"

My understanding is that the use of extended for maternity indicates that she has already had her baby. Am I right?

I am going to send a congratulatory email to her. What should I write? Can you suggest a nice short paragraph? I am just looking for a template?It should be formal since she is the graduate coordinator of our university.

Thank you very much for your time and help

It really could go either way. If there were problems with the pregnancy, such as early labor or a spike in blood pressure, the woman could be out for several weeks (or even months) prior to the baby's arrival. And some people might just start their leave on, say, the first of the month of their due date or the first Monday or whatever, so that HR policies are more easily handled. If my due date was the 5th, I may start on the 1st. (As it was, my due date was the 27th and I was still at work on the 29th. But I wasn't happy!)

Congratulations on your new arrival! My best wishes for health and happiness to you and your family.
Thank you very much Grammar Geek for your useful information.