There’s a pretty decent broad overview of systems thinking (aka complexity theory, the study of complex adaptive systems) in the wikipedia page linked in the sidebar - en.wikipedia.org/wiki/Systems_thinking

I’d say it’s more of a way-of-thinking than anything (so I guess philosophy?), kind of a counterpart to reductionism. In practice, it applies (and has been applied) to basically any field, definitely including physics - early work was very physics focused, but later on the field expanded to include economics and other social science questions. There are models that do use maths/computation (especially some of the earlier approaches), but there’s also a lot of qualitative work associated with it as well.

So I guess the answer to all your questions is “yes”? :)

The first two posts on the community are good deeper introductions to the field.