As of the 2208 update released earlier this month, you won't have to do an online compatibility check to play a game from an XBOX One disc, even if it's offline. You don't need an internet connection to play the game.
The change, which isn't listed as a feature of the 2208 update on Microsoft's site, was confirmed by the Xbox engineering lead, who said that it wasn't necessary in the vast majority of cases.
There is a good breakdown of what the situation was before, but there is a mixed bag when it comes to buying games on discs. The version of the game meant for Microsoft's last-gen consoles will be included in some of the games. Sometimes, the version of the game on the disc is for the Xbox One, but other times, it is branded as working with the other consoles. Before the update, you would have to be online to finish installing the games, so that the newer console could use them.
You will be able to install the Xbox One version of the game straight from the Xbox One or cross- generation disc. You will have to go online if you want to download any updates for the Series X. You have to go online to play games that don't have all of the data on the disc. If Microsoft ever shuts down its server, you should still be able to play the version of the game you have on disc, even though it's not a full victory for game preservation.
The situation for Xbox Series X-exclusive game discs and games downloaded from the store is the same as it was before the update, according to a new video from Hikikomori Media. You won't be able to play it without going online first because the data on those discs "can't be used directly."
Microsoft is trying to make it easier to play games on the platform. Badges are being tested on the console's home screen to make it clear if a game is currently playing.