Yeah, I think you are actually right. I must have misremembered it. This source also suggests Mario Sunshine didn't have a "free" rotating camera but a combination of horizontal rotation and zoom: https://strategywiki.org/wiki/Super_Mario_Sunshine/Controls
Of course the question is whether there might have been an earlier game which had it. Regarding Ico, apparently it also allows only horizontal rotation (camera "panning" is horizontal movement): https://strategywiki.org/wiki/ICO/Controls
I guess then the first game I definitely know that had a free camera was The Legend of Zelda: The Wind Waker, which came out a few months after Sunshine. This is also confirmed here: https://strategywiki.org/wiki/The_Legend_of_Zelda:_The_Wind_...
Of course the question is whether there might have been an earlier game which had it. Regarding Ico, apparently it also allows only horizontal rotation (camera "panning" is horizontal movement): https://strategywiki.org/wiki/ICO/Controls