I think it's more likely that he did exist, but those "details " were exaggerated/fabricated by his followers.
"A man named Jesus (Yeshua) lived at this time"?
Well, certainly. Yeshua was a pretty common name.
"A man named Yeshua was a religious teacher"?
Granted, there were probably several of those
But is that a "historical Jesus"?
I certainly don't think a "historical Jesus"--a man that the stories, exaggerated or not, are based on--exists. The stories are all way too similar to the previous messiah-myths.
I am not yet born, console me.
I fear that the human race may with tall walls wall me,
with strong drugs dope me, with wise lies lure me,
on black racks rack me, in blood-baths roll me.