Visa worries with new company, anyone else been here? So anxious

I'm from India and just graduated from a university here in Korea. I actually just started my first internship at a Korean company! I'm super excited, but honestly, I'm also really anxious about my visa situation right now. I'm on a D-10 visa, and the company keeps telling me they'll handle everything regarding my new visa. But if something goes wrong, or if it gets complicated, I just have no idea what could happen or what to do. As a foreigner, visa issues feel like my lifeline here... it's stressing me out so much. Has anyone else been in a similar spot—starting your first job/internship in Korea where the company handles your visa, and you felt completely in the dark and nervous? What should I be aware of or look out for? Any shared experiences or advice would really calm my nerves right now. I can barely sleep.