This issue was first observed via crxDE: the user did a copy / paste on a node with the .json extension (let's say test.json). After saving, the new node was named "Copy of test" instead of "Copy of test.json".
I tracked the request to the AbstractWebdavServlet.doCopy method - and this is where the .json extension seems to be lost.
The Destination header sent by crxde includes the extension, but the new resource created in doCopy does not have it.
The request looked like this:
To rule out issues in other layers, I tested with the Jackrabbit 2.14.x standalone.
I uploaded the test.json file via WebDav, then executed the following curl request:
The new node was created, but instead of being named "copytest.json", it is called "copytest".