At the time (and I believe also today but I'm not sure) the metal content of coins issued by the US government was set by Congress in law. The law authorizing the minting of the Gold Dollar coins specified they needed to be worth exactly $1.00[1] and, based on the statutory exchange rate of $20.67 per troy ounce of gold between 1849 and 1861[2] (which was also effectively fixed in law[3]), they contained exactly 0.04837 troy ounces of gold (as noted in the Wikipedia article I linked in first reply). Thus it would literally be illegal for the Mint of the United States to debase US currency.

That's why paper money was issued: it was outside of the purview of the Mint and not subject to the legal restrictions on debasement. Referencing [2] again, we can see that at the height of the war in 1864 the market price of gold rose from its statutory price of $20.67 to $47.02 (which, due to the effective disappearance of hard currency from ordinary commerce, would have been relative to the paper currency). In other terms, each Gold Dollar was effectively worth $2.27 in Greenbacks or each Greenback could only buy 44% of a Gold Dollar. That matches up pretty closely with the figure cited in the linked article.

If you were a foreign person holding US gold coins in the Civil War era you could sell those gold coins for their gold content (whose value matched their pre-war face value exactly) even if the US government collapsed. You could not do the same with US paper currency.

[1]https://fraser.stlouisfed.org/title/1094

[2]http://onlygold.com/Info/Historical-Gold-Prices.asp

[3]https://en.m.wikipedia.org/wiki/Coinage_Act_of_1834