Did his siblings see him eat? Did his close relatives or friends see that? Not every thing from a person's life is documented.
Yes, there are many written details about life of Bahaullah, by His companions and people who encountered Him, such as He drinking tea, He dyed His hair with Hanna, He had long hair, He had an unusually long hat,.. to other things such as How fast He was authoring Books. Also, His marriage certificate, passport, and personal belongings are available today. Many people wrote their memories of meeting Bahaullah. But nobody has seen Him reading books, or possessing books. Bahaullah said He did not have books neither read the books people possess.
Among His personal belonging no books found.
But if you want proof, you already provided the proofs and acknowledged that he was educated in it. And "education" doesn't mean that one has to go to a school. Bahá’u’lláh got his education from him studying what is in bold from your post below.
That is a conjecture. Where did you read He was educated?
We no He was very knowledgeable, but the question is not if He is knowledgeable or not. The question is, where and when and how He got His knowledge from?
So there you have it. Historical proof of his education regarding religion and his ability to understand and write in Arabic.
Here's a quote attributed to Samuel Clemmons.
"I have never let schooling interfere with my education."
How Persian classic poetry has anything to do with knowing religious traditions in details? That is like, if when you were a child, they taught you, some classic Shakespeare. Does that make you able to write Bible in Hebrew or Greek, and being able to interpret or know details of other religions?