You want linen, but it’ll still be pricey. Might be able to find something second hand? Linen is capable of truly remarkable evaporative cooling and is amazing for getting rid of moisture and sweat

Okay yeah, that would be my guess as to what that is then. Honestly, not sure why it goes away for you, as my elastane/spandex blend clothes have just been relegated to the “house clothes” category now. I could be wrong but it looks just like it from what I can see.

Polyester does hold on to scents like crazy in my experience. If it’s not washing out try some isopropyl alcohol in a spray bottle and giving it a spritz. Different textiles all have different properties, but I almost always recommend natural fibers for most purposes.

Does the shirt’s fabric content tag mention spandex or elastane or any other stretch material in it? If it’s not 100% polyester and it’s any percentage of stretch fabric, I would say that is the elastic material breaking down and degrading. It can degrade from age, hard wear, washing in vinegar or harsh detergents, or putting it in the dryer at high heat. It’s also completely unnecessary in knit fabrics and I’ll give you three guesses why fast fashion brands like to throw it in everything they make (but I think you’ll only need one).