Here's a detail from a photo of the Conn coat... if it is indeed top-stitched, it is very close to the front edge.
Here's a detail from a similar frock coat at the Smithsonian. No top-stitching, and only some along the base of the collar.
From an 1840s tailor's book: (stitching from the back, or wrong, side), the tailors referred to the particular mode of stitch for edges as a "side stitch."
"The
side-stitch is used for the edges of garments, to keep them from rolling over, or from being drawn out of shape. It is always intended for ornament as well as use, and requires a very quick eye and a careful hand to do it well. In this stitch the needle is passed through the cloth a little above or below the place from which it came out in the former stitch, but it must be at a very little distance from this place, or the sewing silk will be visible on the surface of the cloth, which is a great blemish, and yet it must be far enough away from where it came out to prevent its breaking through, in which case the stitch is lost, both as to use and ornament. Care must also be taken, that the stitches are at regular distances from each other, and that the whole of them are placed at the same distance from the edge of the cloth.
... the side-stitch, and the The only difference between [this], and the back- stitch and fore-stitch is, that the needle is... put entirely through [the cloth], and then passed back again, so as to ensure a thorough hold being taken of the cloth on each side. It is used in thick fabrics, where great strength of workmanship is required.
From the 1880s...
In other words, on the outside of the garment, the head of the needle is stitched to show as little of the stitch as possible, but so close together, and drawn tight enough, that the fact it is sewn is visible, in spite of the lack of very visible stitching.
Some Confederate garments are rather crudely finished, with this edge finishing...