Play away on the console?

I bought a game on the xbox. The money is gone too, but if I want to install the game then I have to pay for it again

What can I do there?

Xbox support: https://beta.support.xbox.com/contact-us

Then you have to write to Microsoft personally and say that if they have an invoice they will give it to you. Otherwise you have to look under your personal games there's also a department for paid games that are not installed