The fields of human-computer interaction, and UI/UX design have experiments.

Testing various compiler optimizations for practicality, etc. are also commonly done.

You list natural language, and natural language processing is a highly experimental / empirical field.

I saw this paper’s abstract and was reminded of your comment: https://arxiv.org/abs/2212.10559

> Experimentally, we comprehensively compare the behavior of ICL and explicit finetuning based on real tasks to provide empirical evidence that supports our understanding

Lambda calculus was an experiment, I'd say. Wolfram's rule 30 too, though granted it's not that significant.

You have to do a bit of science whenever something unexpected comes around and you have to fit it into what you know.