No, factually. Making a background character shine requires a setup. Without setup or plantings of anysort, suddenly making that type of character shine would be bad writing. There was no reason for Carrot to shine in that moment so yeah.. no need to make her shine.
No, I consider this as a introduction of the conflict. A way to make the strawhat shine. Carrot is not a strawhat yet, so there was no need to put her here.
Carrot is supposed to be in the background in Wano so again.. no reason to make her shine here. Like you said, context matter mate.