From watching Kashima Shinden Jikishinkage Ryu, a koryu style of kenjutsu that Takeda Sokaku practiced, in that style at least, breathing methods feature quite prominently in their introductory kata, and at least to an outside eye, seem part an parcel of their approach to power generation.
Chris Covington could add more, I imagine.
Yeah, I'm not at all sure about the koryu part. My guess is that there are some with "breathing" methods. But, for my interest in this topic, I was only concerned with Shioda's teaching and how it coincided with structure/aiki/whatever.