The biological purpose of Fruit is and was to die. Fruit has life, to eat fruit would mean death for that fruit in the sense that it would cease to exist as a living fruit.

Its life energy passed to Adam and Eve when they ate the fruit. In its death the fruit helped Adam and Eve to live. In the process that fruit would "die".

And in the end the seeds of that fruit would return to the earth and give birth to a new fruit tree that would in time and in season give birth to more fruit. A cycle of Life and Death and Rebirth.

Therefore, yes, death existed at the time of Adam and Eve and it existed for a biological purpose.

Geneisis 1:29 Then God said, “I give you every seed-bearing plant on the face of the whole earth and every tree that has fruit with seed in it. They will be yours for food. [New International Version > https://www.biblegateway.com/passage/?search=genesis+1%3A29&version=NIV]