If you choose the texture route, then consider ThruPaint (part of FredoTools) because it is very helpful at texture mapping. You might already know about this plugin, but I figured I’d mention it just in case.
Another useful plugin is “Soap Skin & Bubble.” You can draw the contours of your chair, then it’ll create the curved surface.
I think you’re right that using a texture would be better. Modeling all those fine details would inflate the poly count substantially, which isn’t really worth it unless you’re going for photorealism.
A super quick way is to crop the image of the chair, then make it a 2D face me component. It’s not as detailed, but it’d probably be acceptable for visualization from certain angles. Although, a 3D model would be better for space planning because it has that 3rd dimension.
If you must model the mesh instead of using a texture, then I’d recommend the plugin “Flowify.” You can draw the mesh flat, then use Flowify to make the mesh bend to the shape of a surface.