Waht??>? Sorry but wall to wall carpet is IMO a down grade in any home. As for that look of smooth it is usually in area rugs and good quality woven in silk and for sure not wall to wall . Beautiful silk rugs are an asset to any home any style.

Very soft area rugs sold in inexpensive stores such as Home Goods are often made of rayon or polyester. The fiber content must be labelled.

Wall to wall carpeting sold in carpet stores is usually polyester or nylon. Nylon will wear much better and look great longer. Polyester is softer and will look worn much sooner. Some wall to wall carpet is wool- and quite expensive.

Area rugs at stores will be made of polyester, nylon, wool, acrylic, olefin, silk blend and viscose blend. Viscose, a form of rayon, cannot be cleaned by the majority of rug cleaners so I would advise you to steer clear of those. Any of the other fibers and pros and cons and have different price points.

The current trend is hard surface flooring with area rugs because they can be more easily cleaned. Many still use wall to wall on second floors of homes in bedroom/hallway areas for comfort and sound. This is your decision.

Stanton and Karastan have wool and wool/nylon wall to wall products like you want.

https://www.stantoncarpet.com/