These prompts, especially when automated with APIs and accessed from programming languages, can often become quasi-programming in themselves; for instance, the prompt may include JSON, and the output may include actual parsable code, etc. At other times, these prompts are just natural language, with no trace of programming.
There are 3 SE sites on AI:
one on NLP: https://linguistics.stackexchange.com/
and Stack Overflow if purely about coding.