A user can change the stage's size, e. g. using the mouse. As a result, the shown scene is resized. This means, a scene adopts to the user's wishes.

When replacing the scene in that stage, the stage resizes to the size the new scene requests. This means, the scene ignores the user's previous wishes.

This behaviour is inconsistent. Either it is the user who gives the size (so changing the scene does not resize the stage) or it is the scene who gives the size (so resizing the window by user is impossible). But it makes no sense to override the user's wishes in case there is no real technical force to do so.

This might be by design, but this design is inconsistent and counterintuitive. So I'd say this is a bug. What users want is certainly to keep the user-provides size EVER until the user either demands to get the scene's default size, or he does another manual size change. But literally NOBODY wants wrigging windows!