As a native Spanish speaker that adores music as it represents me in more than one way, I can totally relate to your words. I think “tengo ganas de ti” is all three things you listed in one:
I want you
I desire you
I crave you
I enjoy when the people I care for like learning phrases or words to communicate better with you, and by better I don’t mean in terms of fluency (I speak English quite clearly and fluently) but better as in what those phrases or words mean from the bottom of my heart.
Really enjoyed reading this!