It’s not possible to do it the way you want to. Unfortunately you cannot override any function using extension methods. Extensions methods never take precedence over existing functions with same signatures, they’re only meant to add to functionality, not change it.
You’re going to have to go some other more “verbal” way about it, you could create an extension method for casting it to your own coordinate vector and call it like “ToXZVector2” and/or one that compares also to your custom vector like “EqualsXZVector2” which would return true or false depending on if x and z match.