From Halopedia, the Halo wiki
In the context of video games, backward compatibility refers to the ability of a video game console to play games released for another, older console. Every Xbox console besides the original has been backward compatible with previous Xbox consoles. Consequently, a number of Halo games have been available under backward compatibility.
The Xbox 360 featured backward compatibility with the original Xbox at launch. All Halo titles available on the original Xbox are available on the Xbox 360, with the exception of the Halo: Combat Evolved demo.
At launch, the Xbox One was not backward compatible with either the Xbox 360 or the original Xbox. However, the console was made backward compatible with the Xbox 360 in 2015 at popular request. Backward compatibility with the original Xbox was added later, in 2017.
Xbox Series X|S
In a first for the Xbox console family, Xbox Series X and Xbox Series S were both backward compatible, at launch, supporting every game playable on the previous Xbox console - the Xbox One. This includes all Xbox One games, as well as all Xbox 360 and original Xbox games that are playable on Xbox One. Games with Xbox One X enhancements feature these enhancements on Series X as well, but they are absent on the less powerful Series S.