There is evidence in the Gospels that Jesus could read ...
No, there is narrative in the Gospels suggesting that Jesus could read, much as there is narrative in all manner of prose to the effect that all manner of people could do all manner of things.
Note, for example, this from
The Infancy Gospel of Thomas:
III. 1 But the son of Annas the scribe was standing there with Joseph; and he took a branch of a willow and dispersed the waters which Jesus had gathered together. 2 And when Jesus saw what was done, he was wroth and said unto him: O evil, ungodly, and foolish one, what hurt did the pools and the waters do thee? behold, now also thou shalt be withered like a tree, and shalt not bear leaves, neither root, nor fruit. 3 And straightway that lad withered up wholly, but Jesus departed and went unto Joseph's house. But the parents of him that was withered took him up, bewailing his youth, and brought him to Joseph, and accused him 'for that thou hast such a child which doeth such deeds.'
IV. 1 After that again he went through the village, and a child ran and dashed against his shoulder. And Jesus was provoked and said unto him: Thou shalt not finish thy course (lit. go all thy way). And immediately he fell down and died. But certain when they saw what was done said: Whence was this young child born, for that every word of his is an accomplished work? And the parents of him that was dead came unto Joseph, and blamed him, saying: Thou that hast such a child canst not dwell with us in the village: or do thou teach him to bless and not to curse: for he slayeth our children.
Shall this, too, be construed as evidence, or only that which is properly curated for the purpose of apologetics?
Were there a Jesus (and I suspect there was) there is little reason to presume him illiterate, but there is also (in my opinion) little reason to exaggerate the evidentiary weight of the canonical texts.