Do the Six Authentic Books, such as Bukhari and Muslim, have references and chains of transmission that their authors relied upon in collecting hadiths? And why were some hadiths found in other books, such as the hadith "Whoever recites a letter from the Book of Allah will have a good deed thereby..." narrated by Al-Tirmidhi, not included in Sahih Al-Bukhari and Sahih Muslim?

The "Six Books" (Al-Kutub Al-Sittah) are not all Sahih (authentic). Only Sahih Al-Bukhari and Sahih Muslim committed to compiling solely authentic narrations. As for the four Sunan books (Abu Dawud, Al-Tirmidhi, Al-Nasa'i, Ibn Majah), they narrate authentic, good (Hasan), and weak (Da'if) hadiths for the purpose of seeking familiarity [with different narrations]. There may be authentic hadiths in the Sunan books that are not found in the two Sahih collections, either because they do not meet the criteria of Al-Bukhari and Muslim, or because the two Shaykhs (Al-Bukhari and Muslim) did not commit to including all authentic hadiths, but rather left out many of them for fear of excessive length, as explicitly stated by Al-Bukhari and Muslim themselves.