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.

You’re probably gonna find them through the material. They’re mostly denim or flannel. I just entered “denim shirt men” into my browser and got the shirts immediately. You’re going to look at Levi’s and Wrangler and the like. But why not shop for them second hand, too. They look much better imho if they’re a bit worn. Or please go take a look at your country’s fair fashion stores over those big brands.
I’ll edit the post to clarify, but I’m specifically looking for the lighterweight kind, linen or cotton or something of that weight.