The likelihood is, the writer had no idea about the philosophical ideas around the logos among the Greeks and was instead writing under an influence of the Alexandrian idea of the Logos in Egypt.

For the Greeks, the Logos wasn't a being. It was an aspect of the cosmos that gave it animation and life. It's often equated to god by later writers, but more often than not it is merely an aspect of the universe to describe its mechanisms.

Contrary to that, in Alexandria the great Jewish scholar Philo wrote of the Logos as a person. He called it the "First-born" of God. Here we can see a LOT of bridges to John and other early christian writers. Philo lived contemporary to Jesus and the early church. He died before the two religions formally split off. So the early church seems to have drawn HEAVILY on his writings, far far more than anything Greek.

Just to display this, consider these quotes by Philo, sourced from Oregon State University's library found here

For God, like a shepherd and king, governs (as if they were a flock of sheep) the earth, and the water, and the fire, and the air and all the plants, and living creatures that are in them, whether mortal or divine; and he regulates the nature of the heaven, and the periodical revolutions of the sun and moon, and the variations and harmonious movements of the other stars, ruling them according to law and justice; appointing as their immediate superintendent, his own right reason [logos], his first-born son, who is to receive the charge of this sacred company, as the lieutenant of the great king;

-Philo, On Husbandry XII (45) (p. 178)

God, having sharpened his own word [logos], the divider of all things, divides the essence of the universe which is destitute of form, and is destitute of all distinctive qualities, and the four elements of the world which were separated from this essence, and the plants and the animals which were consolidated by means of these elements.

-Philo, Who Is the Heir of Divine Things XXVII (140) (p. 287)

But the shadow of God is his word [logos], which he used like an instrument when he was making the world. And this shadow, and, as it were, model, is the archetype of other things.

-Philo, Allegorical Interpretation III XXXI (96) (p. 61)

You can see very clearly the heavy influence John takes from Philo. Comparatively, the philosophical understanding of the logos among the Greeks and stoics is simply not the same thing. Other than using the word Logos, there seems to me to be little if any connection to stoicism or other greek writers. For the Greeks and Stoics, the idea of the Logos was simply that of a fire that animates to be used symbolically for how the universe is animated. Aristotle viewed it as simply the human reason. To me, there is little linkage.

It's important to remember that the word Logos is far older than its use in philosophy. So the act of using the word doesn't automatically mean you write it in the philosophical sense. Indeed I don't think even Philo used the word in a philosophical way. Far more like a theological aspect of God in the scriptures.