Does HTML or LaTeX or Markdown provide a computer instructions which are executed? I'm going to take the unpopular opinion and say they are programming languages.
The "program" is the package of instructions that tell the machine what to do. The instructions are written in a programming language.
With a markup language, the markup is the input to a program (like a browser) that tells the machine what to do.
But I think it's not really boolean, it's a sliding scale. Especially with so many programming languages being interpreted or JIT compiled. I think it's less a programming language than many other programming-related things, but more of a programming language than, say, a slideshow.
Yes. Markup-Languages are a subset of Programming-Languages. Turing completness doesn’t matter as things like magic the gathering and habbo hotel are Turing complete
'This markup language isn't even as capable as Habbo Hotel, but it counts anyway because I just called it a programming language.'
There is a literal hierarchy of syntaxes which are recognized by different categories of machine. Programs require a Turing machine. Anything lesser - in a subset like pushdown automata or finite-state machines - doesn't need a proper computer. So it's not a program.
Using modern technology, you can write a C Windows application that runs on Wine that runs on Linux that runs on QEMU running on WASM inside a web browser running on macOS that runs on a virtual machine controlled by a Linux hypervisor. Even the individual instructions sent to the CPU are decoded by a layer of software that rewrites and reorders them inside the CPU. The CPU that may very well contain a smaller Pentium CPU running Minix to maintain operation of the rest of the CPU.
Software lunacy has made low/high-level programming languages obsolete. Everything can be distilled into Javascript runtimes, nothing is a real programming language anymore.
Can you just drop to assembly for what you want to do?
Gnu compilers even have inline assembly, but with any compiler you should at least be able to built a separate, assembly, object file.