What part of the 2012 Toyota Prius exhaust system are these?

That these parts are upstream (@Nevada_545) seems correct. But I looked up along the exhaust system but it wasn’t obvious where it mounted. Also, are these parts reusable or damaged? The edges with the notches seem rough suggested degradation due to rust. Or is it a welded part that broke off?

Finally, if it is intended to improve cat performance, can I assume that if car passes emissions, I do not have to replace it?