I'm having the same issue. Running a fresh install of Win11, new install of the EA App, new install of Fallen Order. When I launch through the app, it launches one instance of the game, then a few seconds later launches a second. Neither instance seems to respect my use of a controller in that the prompts do not change, nor does my cursor disappear despite being able to navigate menus with the controller. The instance will also occasionally flicker or glitch out briefly. This behaviour persists even after terminating one of the launched instances.
I have tried to run a repair on my install of fallen order via the app, however this causes the app to continuously launch new instances of the game until the repair is completed.
Looking at the game install folder directly, I found 2 executables that launched the game: "starwarsjedifallenorder.exe" and "SwGame-Win64-Shipping.exe" Running the Win64 exe after having closed the EA app launches the game, then the app, but no further instances are launched. The other problems persist however, where my controller isn't prioritised.
Launching the former .exe launces the game, then the app and then another instance of the game launches.
I tried deleting both of these executables and then running a repair. the repair brings both back and then reproduces it's previous behaviour of continuously launching multiple instances of the game.