So I got curious and I looked at the compiler source code, and it does a depth-first search.
The fascinating bit to me is that there is a consolidateMultiples function in go/src/go/types/lookup.go (lines 286-304) that detects when multiple embedded types at the same depth provide the same field name. I wonder why they don’t do this for all levels. How deep could this even be in practice for it to matter? You could just have a hashmap with them all.