Crazy that this has even a single upvote and proof that this subreddit is no longer the community for academic discourse it once was. Do you know who Paul Smolensky is? He practically invented the term "neuro-symbolic" and was virtually the only researcher seriously working on it in the 20 years leading up to the deep learning revolution. Harmonic Grammar, Optimality Theory, Tensor Product Representations. Please pick up perhaps any article on connectionism before 2010.

No, this is not a new term for for neuro-symbolic computing (which is now just a buzzword applicable to half of the field), it's a specific theoretical take on how compositional structure could be captured by vectorial representations.