An AI-proof writing tool is a pen and paper, on a glass table, in a Faraday-cage locked room, etc, etc.

Depending on how high are the stakes, weeding off just the most obvious cases of AI usage may be enough. But wherever an electronic input is involved, it can be emulated in ways that are impossible to detect on a reasonable budget. Content analysis may help somehow, but again it would only detect the more obvious cases.