No you should never leave stew out overnight to cool down.
If you leave stew out overnight to cool down then bacteria can grow in the stew and make you sick when you eat it.
So always refrigerate any stew if you're gonna leave it overnight.
Just allow the stew to cool down for 30 minutes and then place the stew in a covered container or covered pot and then refrigerate the stew.
Refrigerating the stew keeps bacteria from growing in the stew so that it does not make you sick.
Stew usually contains meat so you don't want to leave any meats out at room temperature longer than 2 hours because bacteria then grows rapidly on the meat.
So if you left stew out overnight it's likely bad and should be thrown out.
Always refrigerate any leftover stew that you have.
The stew does not have to cool down completely before refrigerating it but just allow the stew to cool down enough which is 30 minutes.
Then refrigerate the stew.
Or freeze any leftover stew and thaw it when ready to eat it.