Exactly this. It probably varies from person to person, but tapping my foot when listening to music at a computer in rythm with the song, or just noding my head slightly makes me way more invested into the song. Doing anything in sync with music is satisfying - that's why games such as Beatsaber or BPM - Bullets Per Minute are sooo satisfying to play - if you don't get dancing, I recommend giving BPM a try.

And dancing is basically the same. You don't do that for others, but to enjoy the music more. And especially with drugs or alcohol involved (because it usually erases any kind of self-consciousness and focus on how you look, so you can focus just on the music), it just feels so great.

And as for ballroom dancing - being so well in sync with someone in addition to the music is an amazing experience. It takes time and requires a stable dancing partner, but once you eventually sync with eachother and know the steps well enough that you don't have to think about it and it just flows, it's an experience unlike anything I've had with a second person. And my dancing partner isn't even my girlfriend, but just a friend.

One comparison I can make is what I had during highschool, where I've wasted several years literally only playing League of Legends with my best friend for all of my free time. We played ADC/Support, and after few hundreds of hours we were so synchronized that we would could instinctively react to each other without thinking or talking about it, and it was a really weird experience. And really interesting, I've never experienced something like that with anyone else (before I started dancing, that is), and it's such an unique connection of minds and thinking that it's an amazing experience.