Formal definition of the Dynamic Array - what is the Dynamic Array
I'm not sure what you mean by this:


  I have never seen, in any programming language ever, any specialized Data Structure called Dynamic Array, nor can I find any ADT which is implemented by Dynamic Array.


There are many examples of dynamic arrays in mainstream programming languages:


Python: list
C++: std::vector
Java: ArrayList
Rust: Vec
OCaml (Batteries included): BatDynArray
Javascript: array (when dense)
and many others...


To answer your question about whether or not dynamic arrays are data structures or ADTs: why not both? Clearly, there is a well-known implementation technique known as a "dynamic array" which is characterized by random-access arrays and exponential resizing. So in this sense, there is an agreed upon notion of a "dynamic array data structure". But also, in many of the examples I gave above, the library interface exposes functionality for explicit resizing (e.g. trimming to size). This suggests that dynamic arrays could be considered as an ADT, because the library interface includes details of performance semantics. And presumably, the "dynamic array data structure" is not the only possible implementation of the "dynamic array ADT".