I don't understand that part of your post
In signing international treaties the PM is acting as the representative of the Queen in Parliament, not as an individual - it’s a constitutional point, which is why treaties don’t have to be approved by Parliament.
So it’s not “Boris” signing such a treaty, it’s the nation.
https://www.parliament.uk/globalasse...office/p14.pdf
“According to constitutional practice in the United Kingdom, Parliament has no formal role in treaty-making, as the power to do so is vested in the executive, acting on behalf of the Crown.”