some resources on compositional thinking
gioele zardini and his lab at MIT are working on building co-design, a system design framework built on a foundation of applied category theory. The WIP book, Categories and Compositionality is an introduction to category theory and co-design can be built from it. MIT subject 1.144: Applied Category Theory for Engineering Design is essentially a survey of this book. I strongly recommend the class if you’re interested in these ideas.
The topos institute is practicing applied category theory. brendan fong and david spivak were both pushing on applied category theory at MIT before starting this institute in California.
Generally for category theory, I think it’s hard to find a concise summary of why some people feel so compelled by it (hence why I thought it might be worth convening). I think Bartosz Milewski’s lectures are quite good at this if you have a bit of a computer programming background. The first lecture is one of the better summaries I’ve found of what the philosophy of category theory might be.