Sounds like all you need is a one-way ticket to some beautiful place without internet for a while. Since you say your manager knows your "current state of mind", s(he) should be fine with a sabbatical...
Yes, two weeks don't help at all. You are halfway through and already can count the days until stress begins again.
I had two burnouts and both took me 2 to 3 months of doing nothing to recover from. I did nothing but have breakfast, watch TV, sleep, have lunch, watch TV, sleep, have dinner, watch TV, sleep. I was not back to normal after these 2 to 3 months, I was only at a level where I could go out and see friends again and think about a real holiday.
I barely avoided burnout 3 by leaving the continent and diving into a completely different culture for more than a year. But here also, the first 2 months were just relaxing. Sitting on rooftops in Fez' medina, at Moroccan beaches or in the desert - always doing nothing more than watching the day pass by.