I’m finding it impossible to shop for these because I’ve only ever bought them in thrift stores and don’t know what they’re properly called.
Edit: Not looking for flannel or denim, but lighterweight fabric, something I’d wear under a jacket not instead of one.
It can be a bit expensive, but you can get custom ones from Proper Cloth in any fabric they sell. They have a few pre-made designs for western shirts, or you can start with the fabric you like and style it with the western details. https://propercloth.com/shop/search/western?sort=recommended