If you lived back then, chances are you’d just straight up remember more things without needing to go look them up again. But, you might also just remember what book you found it in.

Its more the second than the first, knowing where to get info:

• Want to know the industrial products of Turkey? Almanac.
• Who said “Give me a lever long enough and I can move the world” Bartlett’s Familiar Quotations book.
• Synonyms for the word “apology”, thesaurus book. Basic history of the Navajo people, Encyclopedia.
• Definition (or spelling!) of “analgesic” - Merriam Webster Dictionary.
• What happened in town on March 3rd 1967 - Microfilm/microfiche at the library
• What model of refrigerator is the most reliable? - Consumer Reports magazine backissues at the library

I have wondered if this is part of the reason why ancient orators were apparently capable of reciting hours of dialog from memory.

I’d be curious for this answer too. However I think this is more of the “benefits of a classical education” which meant that teaching materials were limited, and you may find your entire class for the year is memorizing famous speeches from men that society deemed worthy.