Xbox series s backwards compatibility with xbox 360 games

That's because it's a 360 game that's backwards compatible with the Xbox One and Series S/X.

The $29 one you saw is the Xbox One version of the game which is backwards compatible with the Series S/X. The 360 version is not backwards compatible.

The 360 version of that game is not backwards compatible. The one listed on the list is for the Xbox One and is compatible with the Series S/X.

If the game you purchase on the Xbox 360 is backward compatible, list here https://www.xbox.com/en-gb/games/backward-compatibility?cat=xbox360 then yes, the game will show up in your library on the Xbox Series S, and you will be able to download it at no extra cost to you. If the game is not backward compatible, then no, it won't work on the Xbox Series S.

If you look at the list on the link I gave you, you will find that Eternal Sonata is not backward compatible, so the only way you can play the game is by using an Xbox 360.

There are a number of 360 games that will play on an Xbox One (as wells the Series X/S). You can check out the backward compatibility list here - https://www.xbox.com/games/backward-compatibility

Filter by the collection on the left (Original Xbox, Xbox 360, etc.)