But Ico indeed used the stick for the camera: https://strategywiki.org/wiki/ICO/Controls
However, I'm not sure whether it was only used for horizontal rotation or full arbitrary rotation (arbitrary combinations of horizontal and vertical) as in Super Mario Sunshine. But it might very well be the first game to have that, not Mario Sunshine.
Edit: Oh, sorry didn't see you mention third person.
Seems wrong too, archived manual (https://archive.org/details/ps2_Jak_and_Daxter-_The_Precurso...) seems to say "RIGHT ANALOG STICK ... Camera Rotate/Zoom" under the game controls. I think the page you linked to is for another game.
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