Jacuzzi is a brand name. I've never seen a Jacuzzi-branded hot tub in a hotel.

The generic term is hot tub.

And while some hotels have "dedicated" hot tubs in a central area, what's in a hotel room is typically only a combo tub / hot tub, which you fill with water each time you use it. (A conventional hot tub has a heater in it and you only change the water after weeks or even months, and use chemistry -- much as in a pool -- to keep the water clean enough in between water changes.)

The ones in hotel rooms, because they have to double as normal tubs, tend to be pesky to use for someone not very familiar with them. You have to fill them just right (both in water level and in temperature) for them to work correctly, and they can take a long time to fill, and so to many people they're more trouble than it's worth.

So I'm not surprised that the ones inside hotel rooms are on the way out. The ones in common areas (which tend to be more like traditional "permanent" hot tubs) are more popular. The younger crowd likes places to socialize, and a common-area "true" hot tub works better for that than an in-room part-time hot tub.

I doubt it's possible to figure out the first use of combo tub / hot tub in a hotel. It was quite likely a retrofit by the individual hotel itself, and not widely publicized. The things you need to retrofit a hotel tub to have hot tub functions are not that different from what you need to retrofit a big home tub to have hot tub functions.

I'm not aware of hot tubs in rooms ever having been a brand staple for any hotel brand. Those hotels that are part of brands, only fraction of the hotels in that brand tend to have hot tubs in rooms, as if it were always an individual hotel decision.