It's worth remembering that evolution doesn't select for the best as much as it selects against the worst.
The reason we have such sensitivity doesn't have to be particularly game changing as long as it doesn't make us less likely to reproduce.
You can plainly see our big niche adaptations being used everyday. We think good. We recognize patterns. We use tools. We walk a lot, efficiently and upright. We communicate with high precision. We have a surprisingly efficient digestive system.
We're not busting out the ability to smell rain super often, which hints that it might be more in the "doesn't hurt" category instead of being a big advantage.
My guess is that being able to smell disturbed soil is helpful for tracking, either where an animal has run or where something has been buried. Our ancestors were not above digging up a fresh-ish dead animal a canine had buried for later.
But it could just be that rain sense slightly more accurate than looking towards the horizon was as useful then as it is now: vaguely, I guess? It just doesn't hurt anything.
We evolved in the Savannah.
Rain means the watering holes are filling up, which is obviously good cause we need water, but it also attracts prey animals.
This, of course, was summarized most eloquently at the zenith of human evoloution: the 1982 hit single by Toto clearly stating, "I bless the rains down in Africa."
I'm still missing something here. For it to be useful, I'd imagine that it would need to inform decisions, and do so where existing senses would fail.
At least in my environment, if I can smell rain, I could also just as easily use my eyes to see the cumulonimbus clouds and say "rain, due east".
In the savanna are there scenarios where the only awareness of rain would be smelling it? Can you derive directionality at 5 parts per trillion? Does it matter?