Near as I can check history, the manufacture of poster girls for science first happens at the start of the twentieth century, but the manufacture of poster girls for computer programming did not happen until much later. Thus history that makes Ada the second computer programmer can be believed, to the extent that it quotes pre twentieth century sources.

Whenever history involves mascots, it should be viewed with suspicion. If people make an undue fuss about a dancing bear, that is evidence that bears cannot dance, rather than evidence that bears can dance. Your prior should be that a mascot is fictitious until proven otherwise.

Ada Lovelace is a mascot, Grace Hopper is a mascot. However Ada Lovelace predates promotion of female mascots, and was the second computer programmer (Babbage being the first), in that she found a bug in one of Babbage's programs.

Babbage wrote, thirty years before it was policy to ballyhoo the contributions of oppressed groups:

I then suggested that she add some notes to Menabrea's memoir, an idea which was immediately adopted. We discussed together the various illustrations that might be introduced: I suggested several but the selection was entirely her own. So also was the algebraic working out of the different problems, except, indeed, that relating to the numbers of Bernoulli, which I had offered to do to save Lady Lovelace the trouble. This she sent back to me for an amendment, having detected a grave mistake which I had made in the process.