The SED had that many members but not all of them were employees. In fact every member had to pay a fee for the privilege of being a member. There was compensation for performing official duties as a party functionary though.

The same is true for the "unofficial workers" of the Stasi. They were generally not paid in cash, though there were exceptions, but most of them gave up their knowledge on their own volition.

The effect on the economy is hard to quantify but the primary problem of the GDR economy was the inefficiency due to the central planning mechanisms and its inherent inflexibility. It is estimated that 1.3% of GDP was spent on the STASI, which is a lot (ca. 3x what the US spends today on all its intelligence agencies) but not in itself crippling to the economy. The examples of China and Vietnam suggest that it is possible to maintain huge and pervasive monolithic parties and a strong state security apparatus with non-crippling effects on the economy.