Eventually QA ends up being owned by either the Engineering team or a standalone QA team. I've seen both work, and both not work. Generally if it's not working for Engineering, it means they're not automating enough or the tests are flaky and they're just ignoring it. If the QA team approach is not working, they're probably overworked... Likely because the engineering org has deeper quality issues they need to fix, but they're trying to make up for it by throwing bodies at it in the QA org.
* We have a no-code test automation product that is used by both QA and Engineers: https://reflect.run