...aaand, after long waiting, two PCBs of detector circuit were assembled. They are identical, except inductor at Pi-network near antenna.

Actually I was quite skeptical, that it will work, after soldering was done, because no tuning was done, no adjustments of antenna length, etc...
I took the dish with steamed beans, placed them into microwave oven and turned it on on maximum power. Then I tried to place the mWessenger PCBA at some distance from oven's glass at first. the on-board LED showed no evidence of life =( .
Then I reduced the distance, holding PCBA in my hand, until it touched the glass of mw-oven from outside. Still no light. The dish with beans was already hot.

"Well, exactly what I expected" - I sighed. However, I took voltmeter to make sure, that idea doesn't work. I was surprised, when I found voltage on terminals of power output, which was greater than 1V!!!
I discharged output capacitors just for any case. Placed PCBA in front of oven's window and turned it on with voltmeter attached. Aaaand.... It works!!! the idea works!.

Today I am satisfied with result of work. However, I still have to solder energy harvesting IC part of project - components and PCBs are in the box. and then we'll see, how much energy can we squeeze out of it....