Interesting that you mention flamenco [1]. I started dancing flamenco 8 years ago, at age 42. I am a late starter to dance, which is a polite way of saying I actively avoided it for most of my life.
When I started, I could barely put together a half-dozen steps. And if I tried to add arm, hand or head movements, my feet went out of time. My brain just didn't feel big enough There was no way I could remember even a tiny section of a choreography like this one I link to from Marco Flores.
Yet as I got more experienced, my brain gradually adjusted to think of body movements as integrated flows, not individual motions. It learnt how to "chunk" them together into logical sequences, and how they align to a piece of music. Much to my surprise, I can now remember complex choreographies several minutes long.
My next challenge is to internalize all of this, so I can relax and dance more comfortably. Maybe I'll never get good enough to improvise dancing with a guitarist and singer. But looking back, I am thrilled how far I've come.
[1] Since few people here will be familiar with flamenco, here is a clip of Spanish dancer Marco Flores performing a Seguiriya: https://youtu.be/ajVmaj6Z93o?t=397.
Notice how Marco beats out what appears a chaotic rhythm with his feet, yet it keeps coming back to the strict beat clapped out by the singer. If you try to follow along, note the rhythm here has a 5-beat bar: 1-and, 2-and, 3-and-a, 4-and-a, 5-and. So the 1, 2 and 5 are short, and 3 and 4 are long.
Also, some versions of the opera Carmen has almost an hour-long flamenco part, it's worth watching, a good french opera.
As a personal experience with ballet for over 5 years (starting in mid-twenties with no prior dance experience, and taking up other modalities later), it has completely reorganized my mind; now I have a strong and reliable memory for body movement, now I have a durable sense of sequentiality that I apply to everything I do (the gains are most apparent when doing many chores, cooking, getting ready for an overseas trip, etc), so that my consciousness is well ordered and doesn't get confused with simultaneity of inputs, but knows how to prioritize easily and without my ostensive effort. It's a bit like having trained a highly capable assistant that now takes over for many tasks that would previously leave my head dizzy with an influx of urgent demands.
Some of this applies to music and learning an instrument, especially not a woodwind, melody-only on, but a coordinating instrument like piano or other strings, especially if you are singing on top of the harmonny. Both dance and music are fundamentally about harmony, in dance you harmonize your body parts relative to each other and to the dance, and in choreographies like ballet, even more so to the other dancers, requiring exacting precision and balance.
Yoga and the classic dances are hard stuff, taxing the mental faculties. It may only not seems so outwardly because so many natural dancers start from early ages, and like learning a language, any mildly talented person starting so early will achieve ease eventually. But building that ease for late starters is much tougher than, say, programming a single page app, if I may be so bold.