They did not.
Their “written records” as such were basically leaves from trees, each having a historical/mythological significance.
The only surviving “record” of Druids was from Julius Caesar written for the “De Bello Gallico” in which he aggrandized the Druids and Celts in order to make his conquest of them seem even more “glorious”.
https://latinitium.com/latin-book-club-julius-caesar-and-the-druids/
The Black Book Of Carmarthen [Welsh] is also a source of “neo-Druidism/paganism”
https://en.wikipedia.org/wiki/Black_Book_of_Carmarthen
Today’s “Druids” are just making it up out of nearly whole cloth.
More is written of the ancient Celtic pagans by the monks who converted them than by any pagan, themselves.
Thanks for the details! I did read Ceasar in Latin, but that was in 1961, and I was too lazy to look up the details.