What is non-duality in Buddhism?
There's a post here on that subject, which isn't long but difficult to summarise: The Dharma of Non-Duality

In the first (main) part the author says:


The word for "non-duality" is advaita
The Buddha didn't use that term (because it was already used then to mean "union of soul with God")
The Buddha did teach "non-duality" is many ways -- e.g. "neither self nor no-self", "middle way", "form and emptiness" (in the Heart Sutra), and "dependent origination implies neither self nor other"
Nagarjuna "used non-duality" in his Mulakarika
Etc.


In a second part (posted as a long comment on the first part), Hans Gruber argues that neither Nargajuna nor the Buddha teach non-duality:


Non-clinging isn't non-duality
Emptiness isn't non-duality, and different things are different even if they are dependently originated
Moving towards liberation (by reducing ignorance etc.) isn't non-duality
The Buddha didn't teach non-dualism as a metaphysical principle, instead he taught dependent origination (also didn't teach anatta as a metaphysical principle or abstract terms, but only as a "predicate" or "practice instruction" applicable to concrete terms i.e. any and all dhammas).


AN 10.29 seems to have the word "advayam" which Bhikkhu Sujato translates as "non-dual" but Bhikkhu Bodhi translates as "undivided". Not sure if this is related.

Yes I expect it's the same root: a+dvaya ("not a pair").

Looking at advaita compared with advaya reminds me of, I wonder if it's similar to, tatha versus tathata -- where one is the adjective (e.g. "true" or "non-dual, single") and the other is an abstract noun ("truth, suchness" or "non-duality") -- or Suñña versus Suññata i.e. "empty" versus "emptiness".

That might fit with Hans Gruber's saying that the Buddha didn't non-duality as a principle (e.g. as an abstract noun).