343 Industries is aware of the issue and a fix is coming.
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There currently exists a bug with Halo Infinite's newly released campaign that seems to impact all players on the Xbox Series X|S. This bug centers around the console's quick resume feature. Specifically, those that make use of quick resume may find that multiplayer cosmetics that are earned through the campaign may find that they are not showing up in their inventories.

Community director at 343 Industries Brian Jarrad says that the team is aware of the issue and it will be fixed. However, he did not provide a time frame for when the issue will be fixed.

For the time being, it is recommended that you fully quit Halo Infinite before re-launching the game from the Xbox dashboard. It's a bit of an inconvenience, but this at least ensures that your unlocked gear appears as it should.

Halo Infinite's single-player campaign launched on Wednesday to some very favorable reviews.