This is a shimano ultegra 6700 rear mech.
The swing arm/cage is incredibly stiff where it connects to the derailleur. I can just about rotate (red arrows) it a small amount but requires a lot of effort.
I tried to loosen up using an hex key (at the blue arrow), but it seems incredibly soft and I think I may have rounded out the thread, it would not budge.
What can I do? Without any motion in that mech cage means that when I shift into the higher gears on the cassette, it doesn't take up the slack in the chain, causing it to drag along the frame and close to the ground.