It sounds crazy, but trust me: a corn cob backscratcher.
It’s essentially just a dried piece of corn on a wooden stick. But the texture is perfect, and because it’s rounded, it covers a much larger area than a regular backscratcher and is much more satisfying to use. My wife bought me one for $11 and I swear by it. You simply cannot go back to a regular backscratcher after trying one.
Oh, and they’re indestructible. My in-laws still use one from 1979!
If your back is constantly itchy, it's possible that you could benefit from exfoliating your skin. I use these salux cloths for my back and all over when I shower. My back scratching tool is now collecting dust and also, my keratosis pilaris issues went away after about a year.