With no configuration whatsoever?
Just pointing to its own documentation…
No configuration what so ever.
No env variables (not even mangohud)
No optimus installed.
Straight up amd-nvidia-prime and gamemoderun.
Edit
I also have lib32-gamemode installed, but that has nothing to do with this, but could be good to have if you run older games I guess.
This is starting to drive me crazy now that I learned that this should not work. Maybe manjaro does something before putting it in the repo?
I dont know what to tell you, it just works. 
Edit2
I know what it is. It’s steam.
I removed gamemoderun from the options, still uses nvidia
$ glxinfo | grep "OpenGL renderer"
OpenGL renderer string: AMD Radeon Graphics (raphael_mendocino, LLVM 16.0.6, DRM 3.54, 6.6.0-2-MANJARO)
$ prime-run glxinfo | grep "OpenGL renderer"
OpenGL renderer string: NVIDIA GeForce RTX 3090/PCIe/SSE2
prime-run is not needed for steam.
So I guess we both learned something today cscs… xD
I have tried both prime-run %command% and gamemoderun %command%.
The result is the same, the game launches but I only get the cursor against a screen that changes colours, no recognizable images. I can clearly hear the audio from the game.
So probably back at what I was saying originally, you’re far from the minimum requirement
The funny thing is that before, when I had video-nvidia installed, at least I could normally see the intro of the game. Now I cannot see it.
Either you would need to nuke the game prefix (delete /home/omano/.local/share/Steam/steamapps/compatdata/1669000/), or force Intel back to run the game (not sure how, maybe remove all Launch Options). Anyway I don’t really think it is worth spending more time trying to debug it. I think your hardware is not good enough to run the game maybe.
//EDIT: report on ProtonDB for same Intel video chipset says:
Can’t interact with main menu and then fades to black
6 months ago
Tinker Steps:Custom Proton: GE
Installs:Yes
Opens:Yes
Starts Play:No
Game launches but can’ t play it
There is no report for same Nvidia card, but both Intel and Nvidia cards you have are similar in performance and features. And now I look at it I think you don’t even have the minimum Vulkan version support on both GPU. Your best bet would be to try to run the game with Launch Option PROTON_USE_WINED3D=1 %command% or maybe PROTON_USE_WINED3D=1 prime-run %command% but it is a wild guess and WINED3D is known to run poorly.
Current Proton requires Vulkan 1.3 feature, your cards support Vulkan 1.1 if I understand.
You may also force an older Proton version in the game Properties → Compatibility Layer.
Try, and retry, different combos of Proton version and Launch Options, deleting the prefix every time to start with a fresh environment when you change something to make sure the prefix itself is not the culprit.