King Frederick II of Sweden

Adolf Frederick was King of Sweden from 1751 to 1771. Two of his sons, Gustav III and Charles XIII, were Swedish monarchs.
Suppose King Adolf Frederick has his third son, Prince Frederick Adolf, Duke of Ostergotland, as his only son and heir.
Thus in 1771 Prince Frederick Adolf becomes King Frederick II of Sweden. What happens then?
 
He seems weak-willed and more interested in playboying (but would he be such in TTL?). He would probably not make a coup, so parliamentary rule would continue during his reign. Finlandish separatism would then not form around opponents to the king, so Finland stays Swedish during the Napoleonic wars, where Sweden might hold a lower profile due to the absence of monarchic rule, although it is unknown who succeeds him after his early death in around 1803.
 
Suppose Frederick II lives many years beyond 1803. He might marry Princess Louise of Denmark, the daughter of King Frederick V and Queen Louise of Denmark.
 
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