I think I agree with everyone. The artefacts you are seeing are down to using box mapping. They seem to appear everywhere where Blender has decided your object transitions from the top to the sides of the “box”. The UVs aren’t being used at all when it’s set up like this. You can confirm this by rotating or scaling or moving the UVs on one of the objects set to use Object co-ordinates and Box Mapping.
The funny thing is that on a real piece of furniture like this you’d expect to see the fabric stretched in certain areas due to the way it is constructed. Best practice for UV unwrapping something like this would be to put the seams on the model exactly where seams are in real life on upholstery like that.
Subsurf can complicate things. There’s a checkbox when unwrapping to take subsurf into account when unwrapping, but that doesn’t always work as expected. It’d be tempted to leave unwrapping until after the model has been finalised and modifiers have been applied. But the issues you were seeing aren’t down to that. They don’t lie along the seams. They lie along the transition point for the box mapping. That’s why there’s a Blend slider under Box Mapping. To blend that transitions. That doesn’t help here though as it would only make matters worse I think due to it being a regular pattern. It works well for more organic textures and grunges and the like.
Maybe have a look around at upholstery stuff and see if you can find examples of the shapes the cut out pieces of fabric make before they are stretched and pinned and sewn into place on furniture look.