If you are unsure whether the additional content has been correctly installed or is not displayed in the game after the download, we recommend following the below steps.

General

Make sure the DLC is licensed for use in the same country as your account. If the countries are different, the DLC may not be compatible.
Make sure you’re connected to the account and signed in with the profile that originally purchased the content.
Make sure you have verified the integrity of your game files.
You may need to update your console or the marketplace. For example, if your download was aborted, you may need to install an update before the download can be completed.
Note that some DLCs included in the Season Pass and, in general, may require an additional download or purchase (with no charge) via the marketplace. Once you have located the content, try downloading it. If the download option is not displayed, the item is not detected as purchased. If the item was purchased or should be included in your Season Pass, please get in touch with marketplace support.
Try reinstalling the game or the DLC (we highly recommend installing/reinstalling the DLCs separately). If the steps mentioned in the article do not work, delete and reinstall the game and the DLC.
If the DLC does not install via the marketplace, ensure you have enough storage on your disk and console. Visit the store to find the minimum storage required for your download.

PlayStation 5 console:

Go to Settings > Users and Accounts > Other > Restore Licenses.
Select Restore and wait until the operation has been completed, then try re-accessing your content.

If the item is displayed as downloadable, but can't be installed, follow these steps:

Check the Xbox status page. If you see any services with alerts, expand the service, scroll down to Notifications, and sign in to receive a message when the service is up and running again.
Try restoring the game's licenses. Xbox > Games & Apps > Warhammer 40,000: Space Marine 2 > Install All.

Here is a guide on how to check if everything is installed correctly:

Go to Microsoft Store.
Find Warhammer 40,000: Space Marine 2 - Season Pass.
Get to the Season Pass page and wait, it should have a Manage button.
Press Manage and wait - Xbox will restore licenses, and you'll be able to download everything within Season Pass.

For game add-ons and other DLC, the first place to check is in your library:

In My Games & Apps, highlight the game (but don’t select it).
Press the Menu button on your controller, and then select Manage game and add-ons.
Select the game tile, and then select each checkbox for which items you want to install.
Select Install, to confirm the installation.

Please get in touch with Focus Entertainment support, the game's publisher, regarding your question.