His lineages are grinding out replications until ...
No "until". The genetic grind never stops and it certainly wasn't aimed at the next "step".
What the experiment showed was that when the environment changed a part of the population was able to adapt to the new conditions.
Your "intelligent design" thinking is trying to read too much into the results.
And if the mutation rate is 1e9, you will have on average only one occurrence of that particular mutation every billion replications.
You got that mutation rate from the informal talk of the group's PopSci outreach video. It isn't real.
And it doesn't matter. When the edge of a gradient had been reached and the environment facing the population changed what happened? The blind undirected processes of evolution allowed the population to adapted to the changing environment.
That's the whole point here. Your mathinations are bogus. Unlike Haldane and others, your math does not accurately model the system you are trying to describe. You are trying to force your desired results into the model.
I can narrow down your estimate from 1 to infinity a little bit and you could as well if you understood how to do the mathematics of evolution.
Why? It doesn't matter. Despite your bogus math averages and probabilities the point stands that when the environment changed the population adapted in pretty short order. And we understand how and why.
So, now that you understand why you don't need antibiotics for drug-resistant variants to appear, why should medical providers be discouraged from using antibiotics?
So besides being ignorant of evolution you don't know how antibiotic resistance became such an issue either.
Do you know how antibiotics work? Do you know why antibiotics are so effective in the human body? Why it's important to complete the full series? Do you understand the interconnections between the antibiotic, the immune system and the rise of resistance? Do you understand that in treatment it is not the antibiotic that finally ends the infection?
Factio Republicana delenda est.