The sinner’s prayer is simply the name that most Protestants use for an act of contrition. It also includes a brief statement of faith, not a full creed, but similar to that.
I had never heard of any connection to the Crusades, however, I suppose that it is possible that something like it might have been used as a formula for Muslims to recite if they were wanting to prove that they were wanting to be Christian. I’m thinking that there could have been a formula for that. It could have been similar to this, but I don’t think it would have been exactly the same.