Hi ne.____.il,
How to unwrap some surfaces correctly is a general question that leads to a long series or two, and even then, it will not answer all questions.
https://cineversity.maxon.net/en/results?term=UV
Thanassis (AKA Noseman) will share many tricks in some series.
There are two main areas: organic and box-like. Sorry, there is no short answer to either of both, or there are some, but they are inefficient when expecting large islands and keeping them paintable.
Thanks for the file.
I would not have thought even to use the unwrap option here, with so many little parts in the border. You showed the path selected inside the book, meaning it is wrapped around, which is not solvable in a straight way. Unwrap would try to keep the surface relation of the 3D object in the same way in the 2D representation. That is impossible for obvious reasons; hence, it is a long story.
As mentioned from time to time, people have tried to fix that problem for over 2000 years, according to the book by John P. Snyder, "Flattening the Earth. It is that old example of wrapping an Orange in a piece of paper; it doesn't work without wrinkles. So, no worries, there is no click-and-go for all cases; in some cases, it will never be. I think I have repeated that now enough times to make you feel more comfortable.
The Original wrap is straight-lined for the larger areas of the book. If you would like to get the new dimensions done, select the UV islands (Select one polygon, then U~W) and perhaps use the UV-Edit> UV Transform to adjust the island's dimensions in this case.
The provided UV solution is usable; stretching the islands individually should do the trick. But first, load an image in, even if it is empty. As the UV space is normalized, always take the whole image dimension from 0-1 for both dimensions.
As a side note, the fastest way with a 90º based object, like a box or a flat book, might be the projection "Cubic 2" or Box, but again, it is inefficient in using the image space.
I hope that helps a little bit.
All the best