For the new US, not much had changed, or was likely to change. If you look at a Committee of Safety musket circa 1788 ( something that a "well-regulated militia" would equip itself with) , or a French Charleville, or a British New Land "Brown Bess", they were not much different from muskets of 50 years before( though the Charleville was in some ways the best design). Percussion ignition would not be adopted until after 1840. The Minie bullet, that enabled rifles to be loaded as quickly as muskets would not come in until after 1850, and even then many smooth-bore muskets would still be used in the Civil War, and a complete change to breech-loading arms would wait until after 1865. Operating a musket was almost the same for a soldier of 1830 as it was for one of 1730.

There had been experiments. For example, Ferguson's breech-loading rifle design was used by the British during the Revolution: but they did not get past the development stage and manufactured in large quantities in armories. One big innovation idea was in the air: the idea of interchangeable parts for military guns, which would enable easier repair of them during campaign. The French had started experimenting with this, and the idea was brought back to the US by Thomas Jefferson when he ceased being ambassador to France in 1789. He would advocate for it, and it would be pursued....but only when the armories at Springfield and Harper's Ferry were built after the end of the 18th c. , and not accomplished until John Hall's shop at Harper's Ferry in the 1820's ( and, despite the legend, not by Eli Whitney). It would then become known as the American System....despite the French origin.

EDIT I should add that the period 1782-1800 saw the Kentucky rifle at its classiest. US gunsmiths turned out some extraordinarily engraved , carved and inlaid pieces, much finer than most of the relatively utilitarian pre-Revolutionary War ones. Whether this was hubris of having won the War, or desperation for gunsmiths having to compete by producing ornamented work because of the sluggish economy has not been established. And though the typical farmer would have been proud of having a fancy Kentucky hunting rifle, this is not what a "well-regulated militia" would have been equipped with.

Hounshell: From the American System to Mass Production