There is currently no way to save changes made with the Warp tool, sorry. Exported JSON files can only be loaded in the City Viewer and it's not a bug, it's the purpose of this feature. When a proper saving/loading functionality is implemented, I'll call it "save" (and "load") instead of confusing "export".
Viewing post in This is GREAT! But what about Import?
Well, it's just that the JSON Export does seem to successfully preserve changes made with the Warp tool, since the 3D Viewer displays the changes I made. Would you be able to save yourself time and effort by using some of the import code from the 3D Viewer to implement a make-shift Load feature? At least as an intentional hack until you make a full Save/Load feature.
Of course, I recognize that this is software which you're sharing with us for free, so I don't want to ask you to do work that you don't have time and energy to commit to. Although, if you could estimate how long implementation may take, and let the community know what sort of rate you would need per hour to live sustainably, I think some fans of your software may be able to reach that target. Is there a way to contribute to you directly through itch.io or another site other than Patreon?
Unfortunately, it's more complicated than that. Those exported JSONs contain enough information to visualize a city (including changes made by the warp tool) but not enough to keep it editable. In your case it would mean that you would be able to import your "warped" city, but not to warp it further after that. It wouldn't be much more than a slightly adjustable image. Actual saving and loading a city is a large task and for this reason it is not implemented yet.