Escaping Strings is not an issue. It's guaranteed about UX. Finding a json in your bio is very likely perceived as disconcerting for the user as it implies structured data collection and isn't just the expected plaintext description. The model most likely has a bias of interacting with tools in json or other common text based formats though.
Why? The explanation given to the LLM seems truthful: this is a string that is directly displayed to the user (as we know it is), so including json in it will result in a broken visual experience for the user.