While searching for a way to get it to run myself, I came across multiple guides that went through the mess of adding the Ubisoft Connect installer to steam as a third party app and installing it, then changing the path to the installed program to launch it through steam. However, doing it this way installed Ubisoft Connect into a different folder than AC Origins, and Connect will not, well, connect the Steam game with the launcher.

1. Install AC Origins (either in game mode or desktop mode)
2. Run the game in desktop mode. It will try to launch UPlay, just exit it. The point of this step was for Steam to create the game folder.
3. Download the PC version of Ubisoft Connect directly on your steam deck in desktop mode.
4. Go to the discover store and install ProtonTricks if you don't already have it. This is what will allow you to install a Windows program directly without having to install it as a third party app through Steam.
5. Find the UbisoftConnect installer (probably in your downloads folder unless you specified otherwise) and run it. If your Deck asks, use ProtonTricks. It will ask you which game it is installing the app for, select AC Origins.
6. If ProtonTricks tells you it doesn't have access to the folder, copy the terminal command it gives you and open Konsole from you "Start" menu. Paste the command and use your digital keyboard to type enter.
7. Ubisoft Connect will finish installing, then open it and log in. Then exit.
8. Run AC Origins from Steam (still in desktop mode), it will launch Ubisoft Connect and link your game to your account, then it will launch.
9. Exit the game, go back to gaming mode and enjoy!