But the Buddha *did* talk about karma, and he did talk about a cycle of births
So yes, he talked about karma a whole lot.
It is almost as though that view of the cosmos, the Vedic view, comes with its own specialized language, and he is translating from "buddha-think" to "vedic-speak", and speaking like a native.
I do wonder why I've never found even one instance in the suttas where the Buddha says "many times in one life".