"Programming" in industry has a very narrow definition though.

Programming is just a way to write down a mechanism. A mechanical computer would be "programmed" quite differently than by writing code in a text editor.

It was stated above that 'a function is effectively calculable if its values can be found by some purely mechanical process'. We may take this statement literally, understanding by a purely mechanical process one which could be carried out by a machine. It is possible to give a mathematical description, in a certain normal form, of the structures of these machines. The development of these ideas leads to the author's definition of a computable function, and to an identification of computability with effective calculability. It is not difficult, though somewhat laborious, to prove that these three definitions [the 3rd is the λ-calculus] are equivalent.

— Turing (1939) in The Undecidable, p. 160

Computer science is most definitely the science of programming machines (computers). It seems ridiculous to me to say CS is not the study of programming. Does CS involve other disciplines like math and physics? Yes. Of course. But it uses math and physics towards the end of programming a machine to carry out the programs.

Let’s consult Wikipedia:

Computer science is the study of computation, automation, and information.[1][2][3] Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (including the design and implementation of hardware and software).[4][5][6] Computer science is generally considered an academic discipline and distinct from computer programming which is considered to be a technical field.[7]

It directly contradicts the narrative you’re peddling. Please, listen to people trying to explain the nuance to you and actually engage. Don’t just keep repeating the same misconception ad nauseam.

“A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically”

“Computation is any type of arithmetic or non-arithmetic calculation that follows a well-defined model (e.g., an algorithm)” AKA a program.

So computation is executing a program. And computers are machines which execute programs.

Turing and the Church-Turing thesis define computability as whether something can be expressed as a program (an algorithm).

Computer science involves math, information theory, and other disciplines insofar as they pertain to programs and programming.

Nobody is arguing that computers don't compute. Why are you stuck on that minutia?

This is patently incorrect. An algorithm is an idea, whereas a program contains a concrete representation (implementation) of one or more algorithms executable on a computer.