Eating halal food

These ahadees do not dictate how ahle kitab or people of book should be doing it. It is telling Muslims how they should be doing it .

Verse 5 of Sura a Miada is not specifying what you can eat or what you cannot eat at people of faith/book. sura Al Inaam verse 121 is not limited to saying name of Allah on animals while slaughtering an animal. You do not eat the raw meat you eat after it has been cooked then it becomes food. Raw meat is not food for Muslims.
It is saying for you can eat food of ahle kitab and they can eat your food. ( now again don’t bring the pig into picture that has been clarified already.)