A quick literature search seems to confirm Gordons estimation, even at the scale of a whole bucket:
[T]he annual mean pH, based upon
samples collected weekly during 1970-1971 and weighted proportionally to
the amount of water and pH during each period of precipitation, was 4.03
at the Hubbard Brook Experimental Forest, New Hampshire; 3.98 at Ithaca,
Raindrops gain a small amount of acidity as they fall through carbon dioxide in the air, but that's not what this question is about. Raindrops commonly start off as ice crystals which have to nucleate around something, usually an aerosol particle such as soot, clay, bacteria, sulphur dioxide , dimethyl sulphide, etc. If a small raindrop nucleates around an ...
These two links were the sources I used when researching this question:
"Mapping critical loads of nitrogen deposition for aquatic ecosystems in the Rocky Mountains"
"Approaches for estimating critical loads of nitrogen and sulfur deposition for Forest Ecosystems of U.S. Federal Lands"
More likely, it works the other way: increased acid-forming compounds in the atmosphere are the cause of more ocean acidification.
Pio et al.  report measurements of sulfur and nitrogen compounds in air masses that they traced to either continental or oceanic origins. They report that the lowest levels of these compounds were from ocean-origin air masses,...
Estimated sulfur release 325 gigatonnes = 325,000 teragrams. The numbers in this diagram are in teragrams
so the release is $\approx 1000\times $ today's annual sulfur cycle.
I think most of the sulfur compounds would be washed into the ocean and then deposited into sediments. I can't find how much sulfur is currently in the oceans, this ...
Essentially no. Acid rain was especially a problem when coal and other industries let up vast amout of sulphur which made strong sulphuric acid rain which could kill trees. Volcanos can also have similar effects, and some industrial regions still create acid rain. There are maps available.
So, as the energy industry becomes solar/wind based, there will be ...
"Cutting the $CO_2$ in half would yield about 5.9."
(A valid approach because we expect reversibility in chemistry and physics.)
[pH of 5.9 for 200 ppm $CO_2$]
Atmospheric $CO_2$ of 200 would be about that of the last glacial maximum. So most of the difference between pure water at pH 7 and 5.9 would seem to be other gases dissolved in air.
Side note: ...