New answers tagged rest
I went with a different approach in the end: Download a complete layer through WFS with outputFormat set to SHAPE-ZIP. What you get is a zipped shapefile of that layer. Import that file back into Geoserver via the restful Importer Extension. Although this might feel a bit hacky, it works quite well for me.
There is no copy facility in the UI, but I believe you could create one using the REST API and a bit of programming instead, just grab both the resource (feature type or coverage) and the layer using a GET request, and then POST a modified version with only the name changed back: http://docs.geoserver.org/stable/en/user/rest/index.html
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