Some of Xbox 360 Games are compatible with xbox one, but not purchasable

you can only see any xbox 360 purchases on a 360, only some of the 360 games are backward compat, so if it aint available to download on the xbox one then it is not BC.

none of the 360 games are compatible on PC.

Backward compatibility 360 games will still be able to be purchased if they are available, since you can purchase them from the Xbox store on the Xbox website or the Xbox One or Xbox Series X|S. Some backward compatible games have been delisted, and only purchasing the disc version of the game (if it has one) is the only option.

If a game is not compatible with Xbox One, whether it's a digital or disc version, it cannot be played on the console. However, some Xbox 360 games are backward compatible with Xbox One, and you can check the list of backward compatible games on the Xbox website. If the game you purchased is on the list, you can download and play the digital version on your Xbox One.

if there from the 360 then you will have to purchase again for the xbox one, some games are backward compatible but only a select few at the moment.

The Xbox One is not backwards compatible with the 360. However, if you decide to purchase an Xbox 360 console again at some point in the future your games will still be available in your download history.