Why do you need to place all this functionality inside the DataGrid Header, instead of placing it above the DataGrid? The layout you are referring to is achievable inside the Header, but requires additional styling customisations, that I personally don't find feasible given the screenshots, especially if you are after some layout responsiveness.
I'd suggest you have a look at these demos to see how to organize your buttons in a responsive layout above the DataGrid.
In addition, if you are wondering what the difference is between RadzenStack and RadzenRow/Column, see this thread - RadzenStacks for everything?