I created a VR experience in Unreal Engine, and inside the VR world, there is a button which can open an external exe, which is also a VR experence. It's like a VR menu room (Unreal application) and a mini VR game (not created by Unreal and is an external exe). When you play the mini game, Unreal VR menu is still open at the back.
I tried different ways to open external exe, such as:
LogHMD: Vision Tracking Acquired
LogHMD: Lost Vision Tracking
Oculus drivers should only handle one process at a time, so whenever that new application is starting, Unreal should give up its connection to the service because someone else is requesting the HMD to render those VR frames now. As a dedicated output, both applications issuing frames at the same time can't be a good thing.
Regarding your context, I suggest you try invoking the
"Stereo On" Console Command to re-enable your HMD, though you might want to also try the Oculus specific
"HMD Enable" command before hand.
Personal concern: Keeping that menu in the background must be consuming resources as well and, in VR, that's an optimization issue you might have to address eventually.