Did Jesus exist at all?

[Mudhammam]

I'm not sure how it adds confidence to the historicity of -any- particular or detail of the narrative.

You mean, I think, the particulars or details that allow interested persons to formulate a rational understanding of the circumstances that led to Christian thought dominating Europe for 2,000 years... in which case such mundane and seemingly insignificant facts are the ends in which we find all investigations into cult leaders who have ever hidden behind a facade to conclude.