I've never met a coherent definition of symbolic AI so I'll just focus on what it contained: some type of search or inference algorithm (iterative deepening, depth first search being major ones) often combined with heuristics written in a programming language like prolog or lisp. Specification + Inference ≊ Specification + Control flow. That means Probabilistic models written in a language like Stan, which is Inference + Specification, fit neatly into so called symbolic AI (which is basically just programming with search/inference).

These search and sampling algorithms still play key roles in game playing AI (chess, poker, Go) and natural language generation. It is the human knowledge, specification and heuristics, part that tends to be more readily replaceable. A lot of control flow and data-structures that powered old AI approaches can be found in databases, compilers, type inference, computer algebra and even the autodiff libraries neural nets are written in.

Video game AI, constraint solving and business rules engines are probably closest to still using the full symbolic approach rather than merely extracting the control flow and structures portion.

We can therefore make a compact prediction: learned approaches replace human written computer programs (specifications, rules systems or heuristics) whenever human contribution is not valuable or is somehow harmful to robustness/generalization.