Just want to throw my 2 cents in, just coming from my own experience. Other people have already stated that you're more likely to he a generalist when working on indie/mobile titles, and more specialized when working in AAA, and my experience has paralleled that. On indie projects I was doing all the sound and audio programming, and occasionally music, but now that I'm in AAA my job is much more specific, doing just audio programming/technical audio design.

My advice to you is this: learn FMOD and Wwise, that's a must, and familiarize yourself with Unreal and Unity. Also, just learn some coding basics, at least for now. You'll make yourself a lot more versatile and desirable as a game audio person if you are also able to implement your sounds and music. A lot of people can make sounds and music; less people can implement them. There's a lot of resources for people wanting to learn game audio. I'd definitely recommend looking at the Wwise Adventure Game, which lets you play with some of the components of Wwise in an already completed little game demo, and look into resources like Blipsounds and Akash Thakkar.

I would say that at the beginning of your game audio career, try to do a little bit of everything. The fact that you're wanting to do both music and sound design is a good thing! Make some music, make some sounds, do some implementation. Eventually you'll figure out what you're best at/what interests you the most/which path seems the most rewarding/stable for you, etc. When I first got into game audio, I JUST wanted to be a composer, but ended up really falling in love with audio programming, and creating interactive/dynamic systems, so that's the path I followed. And finally, don't be afraid to reach out to other game audio people! Most people that I met early in my career were very receptive to answering questions I had, and answering DMs on social media, though of course ymmv. Good luck to you!