Downloading an update for a game while playing another game? Series X

This is an incorrect assumption. You can insert an xbox one disc and download updates that may improve visuals and frame rates on Xbox Series X/S but in order to play you still need the disc unless you own the digital version of it.

Xbox Series X will utilize the Xbox One X version of enhancements while Xbox series S will use the Xbox One S enhancements.

You will not get a free game by borrowing or renting a physical version of a game and installing it on Xbox Series X/S.

Not really...

Xbox Series X games / upgrades / updates has to be installed onto the Series X internal or expansion card SSD,

You can have Xbox One games on your external hard drive that will get an Series X upgrade but the games will need to be transferred to the Series X and then the Series X upgrade will need to be downloaded onto the Series X SSD,

As an example...

I have Marvel Avengers on my external hard drive that will get the Series X upgrade and I will transfer the game over to the Series X SSD ready to download and update the game to the Series X version when available.

@M Bierce

You can't play a disc game while installing another disc game

But you can play a disc game while another is downloading, play a download while installing a disc or play a download while installing another download.

Are you playing a game while trying to update? I've noticed that playing games that rely heavily on internet can stop/slow down the updating or downloading of another game

Hello Drew, sorry to hear you're having trouble with the game.

If you're trying to install the game it may be easier to either do a network transfer or move the game to an external drive and then just attach it to the Series X. From there you should be able to move the game to the Series X and then only need the disc to play the game itself.

As for the discs themselves though check for any scratches that may prevent the reading of the disc properly. Another thing you could try is to take the console offline while you install the game as it's also possible that a game update may be interfering with the install as well.