I purchased sea of thieves in the micrtosoft shop, but it doesn't show up in my library.

I have tried all of the messages you suggested but sea of thieves doesn't appear to show up in my library as a downloadable game, and there is no way for me to download it while using the xbox app and its companion.

No it shows nothing in my purchase history including when I subscribed to the game pass separately before I bought sea of thieves. No purchases show up.

I no longer have Steam on my computer and I got a refund for Sea of Thieves from Steam so it's not even in my Library. I also uninstalled the Steam version of Sea of Thieves from my computer.

You don't need to buy Game pass if you already own the game! The same thing happened to me with RDR2, this is what I went through:

1. Try restarting your Xbox, it might fix the issue of showing it as a "Game Pass" item instead of your purchase.
2. If that doesn't work, go to your Games and Apps > Full Library > All Owned Games. There, Sea of Thieves should show up and you should have the option to install it by selecting the game.

It'll actually just show up in your downloads under the Sea of Thieves game. No codes. Got to My Games and Apps, then Sea of Thieves, hit manage game and it should be ready to install.