Some of the below have been referenced in Chapters of the Primer and other blog posts. Other inspirations have not been hitherto mentioned.
Genesis, Ch. 11 Verses 1-9 will provide you with the story of the Tower of Babel.
[The Wisdom literature of the Old Testament, or similar works of the ancient world, are not a specific inspiration, but are useful reading. The portions of the Codes in the Primer are not written on this model - Punth is atheistic - but it is still in the DNA of the Primer; see below.]
Snow Crash, Neal Stephenson
The discussions of Babel, language and Sumerian culture are more relevant to Punth than corporate warfare, hacking and the metaverse.
Dune, Frank Herbert
The Book of the New Sun, Gene Wolfe
The chapters of Citadel of the Autarch devoted to the Ascian language (if you click on any link in this post, make it the second of these) are obviously vital, but the image of a collapsed space-faring civilisation is also arresting. The Azoth of The Book of the Long Sun is of interest as an artefact of a space-faring civilisation; I have discussed that here.
Nineteen Eighty-Four, George Orwell
The element of Newspeak is most relevant.
A Princess of Mars and the Barsoom series, Eric Rice Burroughs
Various interpretations of which are discussed here.
The Saga of Recluce, L. E. Modesitt, Jr.
Most notably Fall of Angels, Magi'i of Cyador, Scion of Cyador. Discussed here.
Declare, Tim Powers
The djinn of the desert owe a great deal to Declare.
Seeing Like a State, James C. Scott
Reflections on the Revolution in France, Edmund Burke
Red Plenty, Francis Spufford
I cannot claim to have been thinking of any given part of Star Trek when writing on the origins of the Qryth, but as an image of space exploration advanced enough to invoke Clarke's Third Law as well as vigorous enough to produce the Qryth, it serves nicely.
Chariots of the Gods?, Erich Von Daniken
I have not read Chariots of the Gods, but it serves as synecdoche for the whole of the 'Ancient civilisations were built by aliens' school of thought.
Seven Pillars of Wisdom, T. E. Lawrence
More for the atmosphere of the desert than the events of the Arab Revolt.
The Pillow Book, Sei Shonagon