How is the target variable passed to the final estimator in this pipeline?
The Pipeline object performs a .fit_transform(X, y) sequentially based on how you structure your pipeline until just before the last step (the estimator). The estimator does not perform a transform because it's purpose is not to transform your input array X, but to make a prediction. The fit_transform method performs a fit, then a transform on that pipeline step when it is called. In your case that means:

Your standard scalar is fit based on X and y
Your standard scalar transforms your input data X
Your LinearSVC is fit based on your previously transformed X and your un-transformed target y

Since your LinearSVC is the last step of the pipeline object and doesn't have a transform method the process stops. Your Pipeline object that contains your StandardScalar and the LinearSVC now contains a fit version of both these objects. Now you can perform a .predict() method with this pipeline which will cause the fit StandardScalar to perform a .transform() on input X, then this transformed X will be passed to the final estimator LinearSVC for a .predict() which will return your predicted y array.