Did you read the full wikipedia article?
Somebody should start a thread about historical Jesus, because it is actually kind of interesting. It seems a rather controversial topic tbh. Some of the sources in this topic seem to be very influenced by who writes about it.
Like for instance in that Guardian article the writer says their is an abundance of written proof including Josephus, although some of his texts might be altered a bit.
The Wiki article on the other hand states out loud that the paragraphs on Jesus in Josephus' work were added centuries later and clearly false.
First one mentioned is believed to have been altered, but is also believed to have had an authentic nucleus.
Josephus' Antiquities of the Jews, written around 93–94 AD, includes two references to the biblical Jesus Christ in Books 18 and 20 and a reference to John the Baptist in Book 18.
Scholarly opinion varies on the total or partial authenticity of the reference in Book 18, Chapter 3, 3 of the Antiquities, a passage that states that Jesus the Messiah was a wise teacher who was crucified by Pilate, usually called the Testimonium Flavianum. The general scholarly view is that while the Testimonium Flavianum is most likely not authentic in its entirety, it is broadly agreed upon that it originally consisted of an authentic nucleus, which was then subject to Christian expansion/alteration. Although the exact nature and extent of the Christian redaction remains unclear, there is broad consensus as to what the original text of the Testimonium by Josephus would have looked like.
Modern scholarship has largely acknowledged the authenticity of the reference in Book 20, Chapter 9, 1 of the Antiquities to "the brother of Jesus, who was called Christ, whose name was James" and considers it as having the highest level of authenticity among the references of Josephus to Christianity.
Almost all modern scholars consider the reference in Book 18, Chapter 5, 2 of the Antiquities to the imprisonment and death of John the Baptist also to be authentic and not a Christian interpolation
Scholars almost overwhelmingly believe the other two passages that mention people that were close to Jesus are completely authentic.