I have ordered steak diane at a Cajun restaurant and thought it was authentic. It is a cajun version. Grilled tenderloin topped with hollandaise sauce, fresh asparagas, and crawdaddies.
It is quite good but what is it really or is this just a specialty of this restaurant,
sounds like a speciality of this restaurant. I always had Steak Diane flambeed in a brandy sauce with shallots.
Steak Diane is one of those older "classic" dishes, not unlike Red Velvet Cake, in that its origin is often debated, and there are many variations of its recipe.
I do remember, that in the '60's, Steak Diane was considered very chic. In some restaurants it was prepared tableside. A flattened tenderloin type steak was seasoned with salt and pepper, sauteed in some oil and butter, then removed. Some minced shallots were then added to the pan and then you could include some of the following things: Worcestershire sauce, beef or chicken stock, wine, dijon mustard, lemon juice, chopped fresh parsley, mushrooms.... whatever you liked. As an option you could put the steak back in, add a little cognac and flambee it. A showy dish, quick to make.
Your variation is not traditional, as you suspected.