Even though a TV or a player is "rated" to 4K, it ONLY means, it will play video in 4K, meaning Netflix video, Prime video, etc. It also means that apps are NOT going to run in 4K (Some day that will change). This is common on more or less all entry-level players, like the FireTV Stick, Chromecast, and more. So be sure to only use HD images and video when you build content for entry-level players.
Does resolution matter? Absolutely, for example; if you push a 4K photo on a FireTV Stick it will most likely work, but behind the scenes you'll see that the player is using a lot of resources down-sizing that 4K image. So it should be avoided.
Can you run 4K? Absolutely, but you'd have to get a player that actually outputs 4K, like a Windows, Android, RPI5, MacOS, or similar player. Those are the ones we refer to as professional players.