The Quest line of headsets support multiple applications open and usable at once. So does every headset that uses a PC.
Consider how meta originally marketed it in a business setting - would the "virtual office" application allow you to check your private messages in between? This can be built in of course, but currently it looks like an afterthought at best.
I talked to some trainers in a company about VR trainings (my previous company produced such a course). Some trainers were interested in VR because it "keeps trainees from looking at their damn phones"