3V6 Zener Diodes With Very Poor Accuracy
A "zener" diode with a breakdown voltage below ~5.6V are based on the Zener effect and will have a very soft knee, I personally never use them.

The ones with voltage of 5.6 and above exploit the avalanche effect and have a very much sharper knee.

Even so I expect that the diode you have does match its data sheet.

For low voltage shunt regulation either use a series regulator (LDO) or a device such as the TL431 which has a band gap reference, and an opamp in a 3-poin package to create an almost perfect "Zener diode".

kevin