Then show up and see what happens. I think the most problematic will not be the border at FRA (this will likely be counted as transit if you can show tickets and proof of lodging in Mongolia) but your check-in in the US. For the airline concerned, you have a trip to Germany and are not allowed to enter. They will not see your ticket to Mongolia and might not consider this a transit.
Edit: being unvaccinated, you will not be able to do anything in Germany: no restaurants, no hotel.