Let’s begin with the history of Ishtar, yes? She is the Babylonian goddess of fertility, war, love, and sex. Now, let’s keep in mind that Babylonia was an active civilization a few thousand years before Christianity came about. Now, Easter came about during the Second Century, so around 200 AD, long after Babylonia was gone and their texts about Ishtar unfound and untranslated.
Easter on the other hand is COMPLETELY separated from Ishtar. In the second century, Christian missionaries began to come into contact with the Ancient Saxons who celebrated the return of spring and celebrating their goddess of offspring and springtime. This celebration was called Eastre(though it obviously had a Saxon spin on the name because this is the translated name from the Christian missionaries).
In order to convert the pagans to christianity, they needed to absorb the traditions the pagans had without destroying the sactity of christianity. Luckily for them, Eastre fell around the same time as the Christian observance of the Resurrection of Christ, so for them, it made sense to alter the festival of Eastre to fit with Christian morrays, and the spelling also changed from Eastre to Easter.
Now where did the bunny come from? The goddess worshipped by the Saxons was given an earthly symbol of a rabbit. And because rabbits were the most fertile animal that Saxons and Christians new of, that image was also absorbed into Easter as a way to represent new life.
The eggs didn’t show up until after Easter was practiced in the Americas. German settlers taught their children that if they behaved, their Easter bunny would leave them colored eggs.
Now, throughout this, Ishtar has not been mentioned because Ishtar has nothing to do with the modernization of Easter. Easter was a festival taken from the Saxons and molded over time to fit with a changing culture and to absorb more followers.