Mettre en attente is unambiguous in the context of a phone call, that means the audio link between you and your party is suspended. Otherwise, that would be something like je vais vous demander de patienter, ne quittez pas and similar sentences already listed in the other question which do not necessarily mean you’ll be put on hold.

Le bouton hold is not an expression used in France. The most usual name was bouton de mise en attente but that’s a little bit too long to be printed on a key…

At best there might have been phones with “Attente” but I guess most use some kind of symbol like the pause sign ⏸.