Start Modeling

Steps:

1. Open Blender (I used Blender 4.5) and press Shift + A > Image > Mesh Plane and open the barrel_albedo.
2. Go into Edit Mode and select an edge, then quickly tap G + G to "slide" the edge. Align it with the texture.
3. Start adding edge loops by using Ctrl + R and sliding and aligning them with the texture.
4. Let's cut out the gaps between the paper segments, you can either use the Knife tool (K) or beveling the edge to (Ctrl + B) and sliding them in place. While sliding, you can press C once, and it will slide along the normals (indicated by a yellow line). And press X to delete the selection.
5. Save the file. In my case it is in assets/lib/barrel.blend.