Wrote the below before you found stretched cable - still relative...
With the rear caliper, the hydraulic foot brake and mechanical handbrake are separate systems contained in the one caliper - very simplistically put - they pretty much only share the piston for activation.
It is either the handbrake arm on the caliper that is seized (they love to do this), or the hand brake cable corrode and jammed solid -thinking about what you have said about adjustment, the latter sounds possible, but this may have lead to the caliper seizing from lack of use.
To properly diagnose - you need to see what is happening when the hand brake is applied.
First look at the working side, identify the lever and cable, getting someone else to operate the handbrake to see whats happening, now go to the other side see what is not going on - to work out what part you need to unhook the handbrake cable from the caliper, this may require loosening the adjuster -once the cable is released see if its free, if its frozen its you cable, check the arm moves by rotating with grips, careful not to get any on the disk or pads, some lube helps free it up - if this does not move its caliper.
If it is the cable, you will likely have stretched the nearside one, or even the nearside one is likely to loose its seal and go bad - best to replace both sides - look for the Humble mechanic on Youtube he has a great handbrake adjustment video, its a Mk3 but still relevant.
