Several books list what script is used for the written version of each language; IE Elvish, Sylvan, and Undercommon all being written using the Elvish script. That might be helpful for you to determine some kind of language development tree. The 5E PHB has a small list of that type, and the 3E Forgotten Realms Campaign Setting book has a more extensive list of languages and the scripts they use. But I've never seen any kind of "in-universe" language tree like that.
If you're looking to discover some kind of root "Original Language" that all other languages descended from in D&D, I believe that role is supposed to be kind of filled by the Celestial tongue, which is a concept based on the esoteric occult ideas of "Adamic", and of the "Enochian" Angelic script created by the 16th century English polymath and occultist Dr. John Dee.
(I have a pretty cool idea for a character I want to try out soon: a Warlock with the Celestial Patron, based on the aforementioned Dr. John Dee, who is basically a Hermetic Kabbalist and uses a system of magic formed from a patchwork of numerology, divine names, and the Celestial language to draw Arcane magical energies from the Divine power of Celestial entities.)