I am looking for a Leaflet pluging for move (drag and drop), rotate or change a polygon or polyline feature. Also I´d like to capture the feature vertex coordinates once it has been moved to the new position. Otherwise is it posible to do that using perhaps OpenLayers o TurfJS? Which is the most appropiated way to do that, including saving modified feature into the backend?
A quick search found this answer, so your question is possibly a duplicate question:
which leads to this leaflet plugin:
That looks like the answer to your question, minus the getting the feature coordinates, which might be solved by exploring the answers to this question: Coordinates of Leaflet.Draw rectangle
As for saving to the back-end, I would search something like 'leaflet draw save to [backend]'
Maybe more of a long comment.. but:
The Leaflet.draw plugin covers most of the client-side functionality you're after - allowing users to draw/drag/edit etc.
But not rotate, which has been on an open request since 2013.
As noted by @Barrat you can use Leaflet.Path.Transform for rotation, however this won't play too nicely with Leaflet.draw (specifically, in terms of UX - they both provide their own interaction handlers which may conflict).
I've just started a plugin (Leaflet.draw.rotate) to merge the functionality of these two together, however it does not yet support rotating polygons/polylines (it is on the roadmap though).