They used paste food coloring and you don't really need too much of that to get rich deep colors. I know this for sure because i made my daughter's wedding cake, complete with plates, columns and a fountain, and the base color was royal blue, like the blue above, with white fleur-de-lis and curved shell piped decorations. There was no added taste from the food coloring in the icing. No fondant because she hated the taste and having to peel it off, so I found a technique to make icing look as smooth as fondant. Extra work but worth it. Guests wanted to know the bakery because it was the best wedding cake they had ever tasted.
Yes, paste food coloring comes out pretty much the same. Maybe not quite as bright if long baking in oven, but close.
Remember too that the bagel dough rose so not quite as much food coloring as it would appear in the final product.