You don't have to cook the meat before stuffing peppers.
If you do cook the meat first before stuffing the peppers then it will take less time for the stuffed peppers to be ready.
So while you're preparing the stuffed peppers you can brown or cook the meat and then stuff the peppers with the cooked meat.
But when you stuff the meat into the stuffed peppers and then cook those stuffed peppers the meat will also cook with the stuffed peppers.
My mom makes stuffed peppers and always just puts the meat into the stuffed peppers raw and then cooks them.
The meat always just fully cooks with the stuffed peppers.
You can do it either way as it really does not matter.