Origins runs with no problems at all when installed through Steam on the Deck. Steam installs all the required dependencies like physx for you. Haven't tried the GoG or EA versions and don't plan to - but they may require you to install those dependencies yourself going from what I see on the net. Use Protontricks and protontricks-launch to do this.
The game uses a lot of power by default, but a few tweaks will reduce this dramatically and give over 4.5 hours on a single charge.