It was in the 1830s that leavening bread with an alkaline salt first became an important leavening. There was substantive uptake of this modern leavening — calcium carbonate mixed with muriatic acid was the first popular alkaline leavening for bread — in both Ireland and in United States. Less so elsewhere in the Anglophone world. Wild Irish soda bread is still with us as an example of a savory loaf leavened with chemicals, rather than with a living leaven, the chemically Levant loaf bread is now exceedingly rare in United States. It was not always so.
A variety of factors in the United States made it fertile ground for the widespread adoption of chemically leavening — one or another alkaline salt combined with an acid. Depending on the alkaline salt being used, the the acid was either an acidic food, sour milk, buttermilk, or molasses, or a chemical acid like a dilute hydrochloric acid. The alkaline salt that won out was bicarbonate of soda, today as baking soda, and tartaric acid, sold as cream of tartar. Baking powder is simply a mix of baking powder and cream of tartar, roughly in a mix of one part soda to two parts acid, and a buffering agent like cornstarch to keep the two chemicals from reacting well in the can.
Baking soda react instantly upon being exposed to water, so you mix pour into them, mold and bake. Baking powder reacts upon mixing, but there is a second reaction that takes place in the oven. This makes baking powder easier to work with as you don’t have to be in such a rush to go from mixing to baking.
Factors unique to America that encouraged uptake of chemical leavenings for unsweetened dinner breads include a cultural rejection of any sour tonalities in bread dough prior to baking, a total rejection of alcohol and thus a basic distrust of the dough fermentation process, and speculatively, the pressure many women felt to make a perfect loaf. Soda and baking powder breads were more consistent than yeast leavened breads.
How common were chemically leavened home baked loaves? Hard to tell. My guess, based on the advertising text in ads for chemical leavenings, references in books, both pro and con, and cookbook recipes is that it was reasonably common from the 1840s through to the early 20th century.