I agree, this is the thing that stood out to me. There's this kind of amazing leap you have to do to understand how computers do what they do. How does a thing that adds and subtracts numbers paint pictures? Once you grasp that you can transform those things into numbers and then operate on them, the whole world of computation opens up. It's amazing Ada was thinking about this 100 years before computers really existed.
I agree she was a visionary, but take note that by the time she was active, people were already building complex mechanical automata that executed stored programs implemented using cams and gears: https://en.wikipedia.org/wiki/Jaquet-Droz_automata (see also https://en.wikipedia.org/wiki/Maillardet%27s_automaton). I think a small number of very intelligent people would see Babbage's work and Jaquet-Droz and conclude "hmm, if we mash these together with some creativity, it seems reasonable the result would be a programmable automaton capable of painting".
