This scenario is covered in every state I've looked at, including Ohio, with a rule like "A driver must yield the Right of Way to oncoming traffic when making a left turn." The rules of 4-way stop signs are a special case, and do not necessarily apply at 2-way stops.
https://driving-tests.org/ohio/oh-bmv-drivers-handbook-manual/ Page 40.
This explanation can help you see the logic:
At a two-way stop when you’re at a stop sign, you obviously yield to traffic crossing in front of you. But if you’re making a left-hand turn, you’re expected to yield to any vehicle that’s facing you and coming across the intersection – even if you had to wait for traffic to clear and that driver got there after you did. (If that doesn’t make sense to you, picture the intersection with traffic lights. No matter who arrived first, when the light turns green, you always wait for cars to proceed before you make a left-hand turn. This is the same, only with signs instead of red lights.)
In almost all driving situations, when you’re making a left-hand turn, you are expected to yield to other vehicles, including when a driver facing you is turning right.
Here's a video from a driving school that covers the same situation (The second intersection in the video) https://www.youtube.com/watch?v=X4e1XPcDIZ0