The 13mm hex nut(tensioner) is part of a threaded rod that's goes downward and into the back of the tensioner. If it's turning freely, I'd say the rod has popped out of the tensioner and conventional tightening of the serpentine belt is not possible at this point.
The serpentine belt should be snug when it's tightened and you push down on it from the top after everything has been tightened down, to include the 13mm tensioner nut(which seems to be hosed) and the 19mm tensioner locking bolt. My guess is that if you were to retighten the 19mm bolt, you'd have excess slack in the belt. What "might" help until you can repair the tensioning system, is to loosen the long bolt at the very bottom of the alternator(15mm in my case) and tug on the alternator to reacquire some degree of tension in the belt.
If you do not have one, I'd obtain a 124 CD-Rom or the M103 engine manual(hard copy and hard to find).
Your belt tensioning system is not functioning as designed and needs to be repaired.
1991 300-SEL - Model 126
M103 - SOHC
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