I found the documentation page about uploading stories using graph API (it was difficult to find it and it isn't really well documented). I managed to successfully upload an story, but I want to add the link sticker to point to my website.

I think that the documentation doesn't cover that, but some unofficial Instagram tools (buffer.com, socialgest.net) offer that, so it should be an official way to do that (with the internal API is possible, but I don't want to get banned)