Veganism is a philosophy and way of living which seeks to exclude—as far as is possible and practicable—all forms of exploitation of, and cruelty to, animals .........
If you have a budget that allows you to purchase from specialty stores that designate vegan offerings and price is no object, then you should buy foods designated vegan. If you don't have the money or resources than I would not call it practical, and not worry about it.
I don't worry about this, in fact I'd forgotten.
There was a time when I did obsess over all ingredients, and it really affected me mentally. I had to admit that it was unhealthy without any benefit for animals. I believe that if I continued with being that strict I probably would have given up.
Pick your battles. I stay away from things with beeswax or from lac insects if on ingredient list, but I don't give up fruit
The artificial dyes--I don't know. I remember watching for some number, but I don't remember what or why. Many are from petroleum products, like the red dyes