Good article, but there is a frequent misconception of Symbolic AI as "manual creation of lots of rules". This was true for early approaches, such as expert systems in the 70s/80s. Symbolic AI just means, well, AI with symbols, and there are many approaches (e.g., in neuro-symbolic AI or using probabilistic inductive logic programming) where symbolic representations are emergent / learned from data using machine learning approaches and can be uncertain/probabilistic.
In the linked talk "From System 1 Deep Learning to System 2 Deep Learning" by Yoshua Bengio, the speaker first criticizes Symbolic AI only to re-invent concepts from Symbolic AI later (e.g., "high level semantic variables", "shared 'rules' across arguments"), which is rather silly given that some Symbolic AI approaches are well capable of learning symbols, rules etc bottom-up - which is not fundamentally different from learning low-dimensional vector representations or "generalizations" in linguistics.
While the syntax of Answer Set Programming is similar to Prolog, inference in ASP is closer to SAT solving, and ASP solvers are typically extensions of SAT solvers.