Took the cover off today - found nothing (as I suspected). Timing chain fine, not stretched, guide rails fine as far as I can see, hard to say about tensioning but it looked ok to me. No signs of any damage anywhere.
After that I did some googling, and found
this topic. As Will_w202 wrote, it is a common problem, apparently. I pulled the adjuster magnet plug to test - rattle is gone
Now I'm thinking, should I shell out another $500 for yet another adjuster and spend half of my weekend on replacement? I guess I'll drive with the rattle for now
unless it will annoy me a hell lot more.
Thanks for suggestions folks!