Part of my degree was in textiles, and sorry, the above answers are correct. The thicker it is, the more it holds and shows the wrinkles. That’s a characteristic of any natural fiber. One of the reasons that synthetics were developed was just that, permanent press.
The plus side is that they breathe better. Wrinkle free finishes have been developed (cotton), but I haven’t heard of any yet for linen.
One way to test in the store, is take a piece of the garment, squeeze it in your hand and release. If you see any kind of wrinkling that stays, it will be multiplied when you sit in it for a while.
Be grateful for the choice you have in fabric. When I was school, permanent press didn’t exist, nor blended fabrics. I had to wear a cotton blouse to school every day and my HS gym suit was purchased the year before the wrinkle free fabric came out. It was a monkey puzzle to iron. I still have it to remind me, I plan to donate it the school’s museum.