I have now figured out the problem - it was caused by an invalid licence key.
An extension that I had installed on the live site was automatically disabled on the development site because the licence key didn't match the domain name.
When I uninstalled the modification, everything worked correctly.
The problem was that twig variables were being called in the product edit form, but those variables were unavailable, due to the mod being deactivated, causing the page to fail.
I had not spotted this at first - I had tried disabling all of my module extensions but this was a modification, not a module.
Hope it might help anyone else in the same situation - where possible, if your extensions requires a licence key, politely request a second licence from the publisher so that you can use it privately on your development server.
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BTW.: You example illustrates one of many issues with Symfony-Twig: The template engine should not just silently ignore non-existing variables, it should log appropriate error messages!
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