Probably entirely the former. Nintendo's got a history of being overzealous with user health (cough constant game interuptions to tell you to take a break cough), and prolonged vibrations ARE bad for your hands (though I imagine no amount of game controller rumble could actually cause health issues), but the 'motors overheating' thing is entirely silly...

Because the rumble in the joycon2s don't have a motor. There's nothing to overheat, it's a magnetically actuated disk weight. Like, it's a whole thing they're super proud about and have advertised, they can move the weight so precisely using the magnetic actuation that they don't even have a speaker in the joycons, they literally just run the rumble faster so it acts like a speaker cone to make sounds/music with it. There's actually a pretty cool demo for it in the switch 2 welcome tour.