The Hebrew word translated as "breath" in these verses is translated as "spirit" by a few modern versions. It is also translated as "wind" in [Ezekiel 37:9](./09.md).
When Yahweh says that people will know that he is Yahweh, he is implying that they will know that he is the one true God who has supreme authority and power. See how you translated this in [Ezekiel 6:7](../06/06.md). AT: "understand that I am Yahweh, the one true God" or "realize that I, Yahweh, have supreme power and authority" (See: [[rc://en/ta/man/translate/figs-explicit]])