I faced multiple rounds consisting of a screening interview and panel interviews where I was asked technical questions about my field. It was a great experience overall, everyone involved were really knowledgeable about their jobs and I will greatly enjoy working with them

You're right — if rotated n times it's back to fully sorted, so the right half is also sorted and nums[mid] < nums[r] would push r to mid, which is fine because nums[l] would eventually be the minimum anyway. The logic still holds, it just converges to l=0.