It would be interesting to try to have actual registration so that the embossed design can interact with the printed copy rather that just being an arbitrary background decoration.
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Here is a video of a desktop scale embosser used for just that purpose: https://youtu.be/5ZQHSsFnACs?si=DWwgTScwl5HXkwGP
The part where the embossing daisy wheel is shown is at 18:10.
Here are machines used at an industrial scale: https://www.maticagroup.com/technologies/embossers/
They are nevertheless called “embossers”.
Its a far cry from paying by bonk and your phone beeping a few seconds later to indicate your bank has already registered the transaction!