The grounding is a bit daft but it is a left over and changes occur slowly
As for the paperwork your GP can't give you anything as you are fit according to his training and standards. Your AME has grounded you in line with his instructions from the regulator and will be able to confirm this in writing. His letter will effectively say you haven't got a medical so you can't work. He won't though say you are ill. Your employer will accept you cannot operate an aircraft as you haven't got a medical.
They could of course get you to mow the grass!