This could be Fushi no Kami: Rebuilding Civilization Starts with a Village.
When the civilizations of yesteryear fade from memory and become fanciful fantasy, the only evidence of their existence...are books. Ash, a young boy living in a remote farming village, holds a secret—he possesses memories of a distant and more bountiful past life. Days of toiling in the fields have given rise to a burning desire: to bring more enjoyment to the everyday doldrum of his dreary present day! And while books may be the answer, Ash...can’t actually read! But where there is a will, there is a way. Join Ash as he battles illiteracy and sets his sights on a better life!
Synopsis covers the reincarnation aspect. He knows he had a previous life, but doesn't clearly remember anything, and doesn't know how to invent anything on his own. Instead, with the help of the village priest, he teaches himself to read with the intent of learning from the past.
His primary goal is to improve the quality of life for himself and therefore also the villagers.
The village he lives in is definitely poor, with almost all work going into farming and basically no healthcare. There are references throughout the series of people dying of minor fevers or injuries because there's basically no healthcare and not enough food.
There's no magic visible, but there are references to demons. No sex; there is a little gore involving a bear attack. There is a life interest, but it's one sided; the village chief's daughter is blatantly interested in Ash, but he remains oblivious and focused on learning from books. The demographic is shounen.
What doesn't match is the game breaking inventions, but that's rather subjective. His inventions are all fairly minor - new uses for herbs, beekeeping techniques (the beekeepers died before their craft could be taught to their children), literacy for other children and some adults, and a hand cream that can be sold to a trader for profit to buy essentials. There may be other inventions I'm forgetting, but on the whole everything is very subdued.
The merchant bit is also not a good match. He does encounter a merchant who tries to rip off his father by exploiting everyone's math illiteracy, until he corrects him. But that's the only merchant conflict - the merchant doesn't try anything beyond that, and becomes very friendly after Ash invents a hand cream he can sell in the capital.
