[Ali Imran]

It is part of a prayer ritual

Do you know that our 5 times a day rituals are not called "prayer" in our paradigm?

Prayer is called "doa". 

That prayer we do 5 times a day, it is called "solah".

So no, saying the shahadah in our solah is not part of a prayer ritual.

In our solah, we do make "doa" for ourselves, our prophet, or our parents, or friends.