Why won’t my Xbox series x connect to xbox live when trying to playing Xbox 360 games?

It says I’ve been suspended from Xbox live and I won’t be able to sign in when I’m unbanned but the only problem is I’m communication banned and it should have no effect on playing games and it’s on all my Xbox 360 games I play in an Xbox series X but the problem also happens on my Xbox one s and I am not the first user on this xbox. Please fix this as soon as possible.

Also, I’m having the same issue playing my 360 games on my Series S, my Xbox Live account won’t download onto any 360 game on my Series S.

I appreciate your efforts. I know how frustrating this must be. Let's try some steps here to narrow down the issue.

Have you already tried to reinstall the game itself?
How about connecting your console to a different network or internet source?

So I did the hard reset and it still has not worked, I don’t know what else it could be. I’m assuming that means I can no longer play my Xbox 360 games anymore and being able to save my progress. I honestly don’t know why I’m having this issue.

Hi there! This is clearly not the situation I want you to be in. Let's do our best to get this sorted out.

Have you already tried to re-download your Xbox 360 profile? If not yet, let's try it:
While in the Backward Compatible game, press the menu and select button simultaneously to bring up the Xbox 360 guide. While in the guide, scroll down and 'Download Profile' to re-enter your Xbox Live information.

If that doesn't work, it seems like our best option would be to perform a factory reset to remove potentially corrupted data on the console system. There's an option though to keep your games and apps:
Press the Xbox button to open the guide.
Select Profile & system > Settings > System > Console info.
Select Reset console.
On the Reset your console? Please choose “Reset and keep my games & apps”

Kind regards,