I think you're talking about the Difference Engine, but the Analytical Engine was also designed by Baggage.
I'm talking about her notes on the Difference Engine, which included her notes on the Analytical Engine, which wasn't completed until arguably 1991 or 2010, although in both cases the final product included final revisions on the design. I'm not sure why that's relevant, by the way. My comment applies in either case. I'm talking about my linked paper.
What you linked is a translation + her annotation of a description a French mathematician gave of Baggage's design.
Yes, I did link her translation, but specifically I called out her annotation which was more than 80% of the linked document. To be clear: that document served only as a pro-forma translation. It was in fact her annotation that made it notable.
In fact one of the first few things written there is: "Struck with similar reflections, Mr. Babbage has devoted some years to the realization of a gigantic idea. He proposed to himself nothing less than the construction of a machine capable of executing not merely arithmetical calculations, but even all those of analysis, if their laws are known.", so your claim that it was Ada and not Baggage who understood that the Difference Engine didnt have to be restricted to specific calculations is an odd one.
I take your premise to be that Ada was simply relaying Babbage's designs. History is QUITE clear in this regard. Ada discovered the true breadth of the Difference and Analytical engines, not Babbage. Babbage was a wizard with a mind of metal and gears, but Ada understood the implications to the broader field of computation. Babbage himself many times remarked on how she was the one who truly understood what his engines could do. I can't help you if you disagree with this point except to say you should please research the topic - Babbage himself has remarked on this many times.
The Analytical Engine was Turing complete.
Yes, I agree. And? It was designed with her input, including especially my above citation. The concept of Universality was not yet established. My point is that Babbage did not give to the world a Universal machine, he gave a very useful but very expensive calculator and the blueprints to build a much more general computer.
Finally: Ada's contribution to modern computer science is that she was the first person to take a concrete, physical machine and use it to calculate results based on established mathematical algorithms that weren't part of the machine's specifications. She also firmly established Punch Cards as a means of programming such machines.
I hate to employ ad-hominem but I want to drive home this point: if you can't see how that last paragraph implies that Ada made a lasting and real contribution to modern computer science, then you must be willfully ignorant.