The fact that somebody set down information about a person whether in a religious book or not and presented it in a way that suggests he meant it to be taken as non-fiction is evidence of the existence that the person described existed. It might be weak evidence and without corroboration it doesn't approach proof that the person existed but by my definition of the word, evidence, it is evidence.
Well ... you have to be careful to ensure that what you call "evidence", is actually evidence of that which you are claiming. As opposed to being evidence of something else entirely.
In your above example - the fact that, as you say,
"somebody set down information about a person in a religious book", is not evidence that what he set down about that person was actually true. And the fact of whether the writer may or may not have, as you say,
"meant it to be taken as non-fiction", is again not evidence that the writer was either correct in what he wrote or even telling the truth about what he wrote. What the author wrote is not in itself evidence of the truth of which he writes.
What would be evidence that the author had indeed written truth, would be something verifiable as a fact supporting what the author had said. That's what is needed to make it evidence of that which the author claims ... not merely the authors written claim itself.
However, in the case of Paul's letters and the canonical gospels, what those authors wrote or preached about Jesus, whilst no doubt at the time considered so wonderful that it simply had to be true, has since been discovered to be physically impossible. Their descriptions of Jesus do not merely contain one or two claims which are probably untrue or fictional. They are absolutely packed with claims that are now known to be completely untrue and impossible supernatural fiction.
Afaik, there is actually nothing at all in that biblical writing which is evidence of anything other than the authors religious beliefs. Certainly not any evidence presented to show that their beliefs about Jesus were ever true.
But against that, the continuous mass of highly incrementing impossible claims, is most certainly "evidence" that none of those biblical writers should be believed in anything they wrote in the bible, unless there is very clear and verifiable external independent non-religious evidence to confirm any of it.