Why is Unity Game view still showing only one eye after switched to "Both Eyes" mode?

Question

I encountered a problem when developing a stereoscopic project with HTC Vive Pro Eye and SteamVR on Unity v2022.3.

After start running in the Unity Editor, even if I switched the Game view to Both Eyes, the view still kept a monocular view, although the display actually seen in the HMD was already stereoscopic as expected. I have tried adding

XRSettings.gameViewRenderMode = GameViewRenderMode.BothEyes; 

in my script but it didn't help. See below image

where the difference between eyes is the purple, eye-tracking gaze ray.

Then I found the Project Settings → XR Plug-in Management → OpenVR → Mirror View Mode options which seems to relate, but it didn't provide a Both Eyes option

The Left or Right options only determined whether the Game view keeps at left-eye or right-eye display. The None option would totally shut off the Game view, while the Open VR option seemed to turn the Game view to a mix of both eyes and also impacted the SteamVR preview

Now what can I do to recover the Both Eyes mode in the Game view?

PS.

Interestingly, this project was updated and reconstructed from a lower version of Unity (v2019.4). In that older version, the Game view could display the Both Eyes mode normally

and it even did not have a XR Plugin management package

In all the cases above, the display inside the VR headset was always normal and stereoscopic as intended. The problem was only regarding the Game view.