Side note: you might be better off using said sauces at the end of your fry when your dish is basically done, not to replace oil but just for flavor (and to cook some of the vinegar out of said sauce). I do that with some Japanese barbecue sauce when frying vegetables, but it’s also a thin/vinegary sauce (I wouldn’t try it with something made for dipping).

Both of the proposed have ingredients that cook and char to solids if you cook them at temperatures you want to fry at. You need something that can take the heat and transfer it. You need a fat or an oil. Maybe a heavy sugary water like applesauce could be used but it’s not boiling than frying.

Both are not oil, they are condiments. It will simply burn and char before any reasonable oils smoke point.

You can’t fry with any water-based liquid, as those can only heat to the boiling point of water, and once that’s gone they’ll burn

Are you all out of oil?

Teriyaki can not be.

I don’t know what magi is.