Most cases of prompt injection are harder to fix, and the success of the products they occur in relies on engineers who should know better sticking their heads in the sand about security risks.
Mitigations would include ensuring it doesn't have that agency, and adding framing text to the reply, and perhaps disabling Markdown formatting of the reply.
But also, the leak is being talked up quite a bit:
> Private video titles aren't just metadata. They can reveal unreleased content, unannounced projects and sensitive personal material.
Putting "sensitive personal material" in the title of a YouTube video upload and relying on YouTube to keep the video "private" seems like a terrible idea in the first place, and at best pointless.
Even if it's just a non-clickable link to "more information", some data can be exfiltrated that way.
By this standard, we shouldn't allow comments on YouTube. Or perhaps anywhere.