How to understand the complexity of Kruskal implemented with Quick-Union by rank and path compression?
You are absolutely right.  There is nothing wrong with your reasoning.

The running time of Kruskal's algorithm, when implemented in the way you describe, is $O(m \log m)$, or equivalently, $O(m \log n)$.  If the book says its running time is $O((m+n) G(n))$, the book is wrong; that doesn't take into account the time to sort the edges by weight.

If you look at other sources I think you'll find that they correctly report the running time of Kruskal's algorithm.