Starbucks isn’t special here, it’s a waterproof cup. I always assumed it was some kind of wax too so I also had a flashback to all the paper cups I threw in a recycling can [0]. But on second thought, what kind of wax deals well with water at 95C ? They’re all plastic coated.
[0] I guess most recycling is land filled or dumped in the ocean anyway, so my sins didn’t affect much of the outcome
But all food containers are like that. They are not recyclable. In fact, MOST things that you'd expected to be recyclable are not. Your bottle doesn't have a cap on? It will sink in water and end up in a landfill. Glass other color than clear? Landfill. And so on.
[0] I guess most recycling is land filled or dumped in the ocean anyway, so my sins didn’t affect much of the outcome