There are several different ways to do this, but I’m not feeling well today and I’m going to have to leave it to other people to go into most of the details.
However, by far the simplest solution would be to put a smart switch cover over the existing wall switch which physically moves the dumb switch underneath. That switch cover can report its on/off status to smartthings and you won’t have to change any wiring in the four-way or the outlet.
There are two that work well with smartthings. Both are battery operated devices that fit over the existing switch and physically move it. Both are also on the official “works with smartthings“ list, which is a plus since they should work straight out of the box.
The ecolink is a Z wave device. Prices vary a lot, so shop around. There is one model that fits over toggle switches and a different model that fits over rocker switches so check to make sure you are getting the right one.
The Third Reality is a zigbee device. It comes with an adapter so the same model can work with either a rocker or a toggle switch underneath.
Neither of these are particularly aesthetic choices, but they work well and solve retrofit problems where you don’t want to do any wiring.
We should also note, though, that both are fairly noisy, about the same as a smart lock, because they are physically moving the device underneath. So that’s another consideration for this option.