Whenever I create a new window, I get a completely new set of tabs (empty at start). Is there a way to share the previously opened set of tabs among these splitted windows without needing to open any from the new window ?
I believe you’re looking for https://www.sublimetext.com/docs/tab_multi-select.html
Maybe groups are what you want?
A window can contain multiple groups of views in different layouts such as 2 columns, 3 columns, … .
See: Menu > View > Layout > …