Update: I went back in the spring of 2021 to take more detailed pictures of the convent.
I realized I had actually visited the second location of the Carmelite Sisters of St. Joseph out in Ladue, which is where they moved when Soulard was becoming too industrial back in the early Twentieth Century. Or maybe I should say, people’s tolerance for industry was getting lower. It’s a beautiful building, restored nicely, and is a great example of a convent building from the mid Nineteenth Century when most have been demolished. You can see the chapel from the last photo in this post all the way back in 2007.
There were other convents in Soulard, including the Ursulines on Twelfth Street at Russell.