A lot of ink has been spilled on the topic of the cross. The WT felt it had uncovered some deep conspiracy when they found a number of words were used to describe how Jesus was understood to have been killed. There was an extensive thread many years ago that in short strongly supports the conclusion that at least some NT writers envisioned a cross, while others had a tree in mind. The point is simple, it was an evolving idea (even while the NT was being formed) that may well have been influenced by the Roman tradition of crucifixion while perceiving a tree in the earliest layers of the legend. Again, we will never know.
Went to the Louvre last week and saw this famous statue. It's a scene from the Dionysus myth. Zues has sex with a human and has a son. Hera his wife is very angry and tries to have him killed. Zues hides him and has him tutored by a wise old Satyr named Silenus who raises him like a son. Eventually Silenus is bound to a tree and killed. My point is not to suggest direct lifting of the Jesus story from the mythos around them but that these traditions were certainly in the air. Does it matter? Nope.