Purchased BC game not showing in Ready to install

It happens to me too since last week, when the game dissapeared from my owned library (i have a digital copy). I think it's a store glitch, because if you use the search engine in the store using the words "prince of persia", it gives as a result every
game except for this one (it happens both in the console and in the web page), so you can't re-download it. I contacted the xbox support, so i hope it gets resolved.

If it is showing as a Backwards Compatible game then yes, once you purchase the game it will be ready to download on your Xbox One. It should be under Ready to Install once purchased. Any BC Game shown on the marketplace will be playable on your Xbox One.
I personally have downloaded quite a few.

Once your digital game is BC, it will show up in the ready to install column.

GWG titles are only free during the month they were announced for as for BC if you dont have a 360 the only way you can currently download them is through xbox.com, although phil spencer has stated they are looking into a way to directly purchase the games
on xbox one, any game that you have got already with GWG thats BC will show up in your ready to install section.

if they were the PopCap games (peggle, zuma, heavy weapon, feeding frenzy), then this was a known issue. it was caused by a glitch when adding those titles to the EA Access system. this caused the games to show in the Ready to Install list for many users
for a short period of time, but it was quickly remedied. anyone who installed these games without having a subscription to EA Access was not granted an ownership license, and will not be able to play them without purchasing.

also as Daft Badger has mentioned, new games get added to the Backwards Compatible list all the time. anything you have purchased on 360 already that is BC will show up in your Ready to Install list, so potentially new games could show up again in the future.