Games disappearing from Ready to install list

Unfortunately the games disappear from both Install and Ready to Install lists

I would reach out to customer support and explain to them that you bought the game but it's not available in your library.

https://support.xbox.com/en-US/contact-us

That's not accurate info, You can use the same console to play games with your account, But you can't sign in as someone else on your console and use their games, Even if they are family

This is exactly what Home Xbox is for, to share all the games you own with your household. Not with strangers or friends but within your household.

My suggestions would be to:

Check if you are using the same account that made the purchase,

Check if you have hidden the titles from the Ready to install list

Check if you were gamesharing

Yes, and this is where the lines start getting in the "grey area" as they call it. You only get 5 home xbox uses a year. They are meant for your home xbox. Not your brothers/sisters or extended family. When you designate a console as your home xbox.
You're saying it's YOUR home xbox and that you will be using it as your main Xbox. If you sign into your brothers Xbox and make it your Home ( just an example) And your brother makes purchases, uses your account and gets a ban, collects account info while
you're signed in and not looking, Then uses that info later to do anything unauthorized guess what? There is no recourse, You are 100% responsible for all of that. People lose accounts all the time, even to family members, People get bans all the time, because
of family members. A lot can happen, which is why they don't allow it. Even with family. There is a "grey area" and some people find ways to work around things, But it's risky and not encouraged

There are always grey areas.

However, "your brother" should never be logging in as you, your account doesn't need to be on that console. They should be using their own account.

As quoted from Xbox "The console designated as your home Xbox is where you can share games and some content with others who sign in (with their own account) to that console". You are most certainly NOT
sharing your account and never should.

Of course there are users who will try and bend the rules beyond where they should be, and they should indeed be punished for it.