4K (or a hypothetical 8K or a 16K) AppleTV will work fine with a 1080p TV. Hardware capable of more works just fine with screens capable of less. If I'm not mistaken, your AppleTV can be hooked to a 720p or even 480i TV and display as good as it can look at 720p or 480i. Similarly, I believe all of the new M4 Macs with TB5 can drive an 8K monitor... but can use a 5K or 4K or lower-res monitor just fine too. I would guess that very, VERY few of the new Macs that have already been purchased are connected to 8K monitors.
What you will get when you buy a new one is faster UI, faster everything else, broader app compatibility (as apps for that one will increasingly be dropped). That's not necessarily a reason to buy a new one until you need to replace it... but just trying to get the concept across that the "4K" reference doesn't force anyone to own a 4K TV too.