Hmm, to me as native speaker, 'sonst' has pretty much only one meaning which is pretty much exactly 'or else'. There's a longer and 'more archaic' version 'ansonsten'.
Forgive me for trying it out on you:
“Er trinkt heute Kaffee, sonst trinkt er nur Tee.”
Forgive me for trying it out on you:
“Er trinkt heute Kaffee, sonst trinkt er nur Tee.”