Ömer is strictly masculine and have nothing to do with Ömür. They are both derived from Arabic but Ömür is a unisex and modern name while Ömer is a classic. Its namesake is Khalifa Umar. You can't see just one Ömer as a girl or woman in Turkey. We use "ömür" in our daily language as "lifetime".
Ömer is also used as a feminine name in Turkish. A variant of this name used for both genders is Ömür. However, Ömer is more common for males. So, I think that the "Gender" of this name should be changed from "Masculine" to "Masculine & Feminine".Sources: https://forebears.io/forenames/ömer https://forebears.io/x/forenames/ömür