Hi,
Thank you very much for all the details and your kind words!
The search requests the URL for each element via the standard get_permalink function, which should always return the appropriate permalink registered to the element.
I’m guessing that the structured data plugin is likely registering these URLs somewhere, but it may not be directly to that hook so it doesn’t propagate.
There is very likely a way to somehow get that URL programmatically via a function. I have looked up the plugin documentation but I couldn’t find any API or function reference to start with.
Can you please ask them via their support how to get the permalink programmatically via the FAQ ID? With that information I can construct a small custom coded snippet to replace the URLs with the ones generated by the plugin.