You remind me a bit of myself many years ago.Let me tell my story just because it has led to a life with musc ( though not as a profession,) and what you might consider financial stability. I was seriously considering conservatory when I was in high school, though in voice, not piano. My teachers thought I could get in, and that’s what everyone who knew me though I would do. I also really liked math and academics in general. Well, I was a first generation college student and so I eventually decided I just wasn’t confident enough, especially in terms of financial security or practicality, to gogo the conservatory route. I ended up at Yale, where I majored in math and physics and, yes, took lessons and participated in musicals and light opera ( we have a Gilbert and Sullivan Society. Lots of fun!) I then went to get a doctorate in Applied Math. I still took lessons though not as often, and played / sang in a band that performed at coffee houses and some clubs.
My " adult" life has consisted of being a math professor ( with tenure, lots of security) at a college that has an excellent music program as well.
Not saying this is the path for you or anyone, just in my case it certainly let me continue music,at least to some extent, and yet have a good, satisfying, job that many would consider financially stable.
If you are interested in a math major you might also want to consider a career in actuarial science ( beanactuary.org is a good site with lots of info) or operations research.
I apologize for the length of this post, but the original poster’s question really resonated. Hope my story and thoughts can help some folks!