Game capture sharing

Try going into Settings, Preferences, and then Capture & Share.

From there check to see if under Capture in the first block that says, "Allow game captures", and see if it either shows: "Captures by me or games" or "Capture by me."

If it says, "Don't capture", then change it to either one of the other two options.

To capture gameplay either before or after the fact, follow this guide:

https://beta.support.xbox.com/help/friends-social-activity/share-socialize/capture-game-clips-and-screenshots

How do I share from my console?

You can also share your clips directly from your console:

1. Select Broadcast & capture from the guide.
2. Select Capture > Manage captures.
3. Choose the game clip that you want to share.
4. Select the Share to icon.
5. Select from the list where you’d like to share your clip: to your activity feed, in a message, in a club, on Twitter, or to OneDrive.

Do you mean shared content as in game captures, like clips or screenshots?

Um.. You could try going to settings, general, volume & audio output. Then change the party chat output to headphones and speakers. Then try to record a clip and see if its better.