A few months ago, Apple changed their policy to no longer require membership in their $99 developer program in order to test apps on Apple devices. This means anyone can sideload apps onto iOS devices without having to pay Apple or jailbreak their device. The new Apple TV runs tvOS which is heavily based off of iOS, so it’s likely these same new lax rules for loading unofficial apps also apply to the new Apple TV. This may mean that it will be possible to sideload Kodi onto the new Apple TV without jailbreaking.
If sideloading Kodi onto the new Apple TV is possible, the process will be significantly more difficult than sideloading Kodi onto the Fire TV or Fire TV Stick. For starters, it will only be possible with an Apple computer. You will need to use Xcode, Apple’s development software, and compile Kodi yourself using the app’s source code. Even if you have the required Apple hardware and the proficiency to compile your own Apple TV software, there’s no guarantee the current iOS version of Kodi will work for the new Apple TV. If that’s the case, I’d imagine that supporting a device with such a difficult installation path wouldn’t be high on the Kodi team’s list of priorities.