Where are the existing pipes? Are you moving the plumbing?

The long copper pipe at the bottom of the main wall, and to the right bottom corner of that wall we also have a dryer duct.

These lines

Your best bet is to hide them in the cabinets with faux backs inside the cabinets. It doesn’t make sense to lose the width of the pipe all along the wall due to the copper pipe.

Or you could have slightly deeper counters and pull the cabinets out from the wall a few inches, if everything you need to hide is below the counter height.

Building on what @artimis78 suggested, you can install custom reduced-depth base cabinets along that wall. That way your countertop depth would be standard if that is what you prefer.

The copper pipe could be replaced by pex run through the existing wall studs.

Have a plumber run the pipe up and over, through the ceiling joist. Costs the same as or less than building out the wall.

We are building out a wall in our kitchen because the wall is literally plaster directly on masonry between the two houses. But we are building it out by using 2x4 on the flat so we are using only about two inches. That may be an option. But to me it looks like the suggestion to pull the cabinets forward a bit and have a slightly deeper counter will work.