Just quickly made a plugin to fix the problem.
It is not in the community plugin catalog yet. Already submitted. You can download it on my GitHub repo page.
If the selection is empty (just a cursor, no text selected), a tab will be inserted.
If text is selected, you can decide to replace selection with a tab or indent the selected lines (like in just about every IDE, tab indents, shift tab unindents) in the plugin settings page.