Legitimately

Physical

Any disc will work, no problems here. All episodes entitled to your disc (see: about each version of the game) are downloadable from the Microsoft store on Xbox One/Series consoles.

Note: The discs are not region-locked, but the episode downloads are. Change your Microsoft Account region to the region of the disc if you cannot download the episodes.

Yarr!

The Xbox One and Series consoles have a sandboxed "developer mode" accessible to end users. An excellent guide on Reddit explains how to access/use it.

1. You can't run the Xbox One version of the game natively, but you can emulate the Xbox 360 version. Download a copy of Xenia Canary (an Xbox 360 emulator) from the Xbox Dev Store.

2. In Dev Mode on your Xbox, navigate to your IP address under "Remote Access Settings" and enter it into your web browser. You should be brought into the "Xbox Device Portal".

3. Click "add" under "My Games & Apps" and choose the Xenia .appx file. Press "Start" when prompted for dependencies.

4. Back on the Xbox, press the Select button (the button with the two squares) over Xenia. Select App Details > App Type > Game.

5. Go to the Xbox 360 page and download the Season One files. The install process is different to the standard Xbox 360.

6. Extract the Season One files + episodes onto a USB drive and plug them into your Xbox.

7. Open Xenia, go to paths and add the MCSM S1 folder. MCSM S1 should eventually show up in your games list.

8. Click X over MCSM, select Manage DLC and install everything in MCSM's content folder. Do the same for the Title Update.