I was wondering if there is any way to bind a keyboard shortcut to this exact button in the IDE.
I can't find it in: "options > configure TexStudio > shortcuts"
I have taken the time to email Benito van der Zander, the maintainer of TexStudio: https://texstudio.sourceforge.net/
Here is his answer:
I do not think so. You have to right click on the section to choose the section. Even if there was a shortcut, it would not know which section to indent. The current selection can be indented with tab.
So it is impossible as of 2022 December.