Hi Pavel!
Is it both cables that appear "welded", or just the one?
Have you tried turning one or the other of the adjusting screws in to see if some slack can be created? Do the adjusting barrels turn at all?
Can you wiggle the shift barrel any?
The reasoning behind the above is, if there is a bit of slack, the free cable might be used to gently leverage the one that is stuck for whatever reason. With the present problem, it seems there's no slack in the system, which is worrisome in itself.
The PB Blaster should have had some effect by now, having soaked a couple hours, though it could take overnight. I have in some cases waited a week, reapplying it daily. That stuff really does work great on galvanic corrosion.
I'm still leaning toward the known (frayed cable), in part 'cos like you, I can't imagine the mechanism by which it could have galvanically welded.
Best,
Dan. (...who openly admits to bafflement in this case)