Because Karl XIII is a nephew of Karl XII and not some elective nobody?The Swedish part.
Because Karl XIII is a nephew of Karl XII and not some elective nobody?
It does not matter who he is. Sweden became the Great Power due to a combination of the very specific circumstances which did not exist in the mid XVIII and even at the beginning of that century when it was convincingly demonstrated that even a highly competent Swedish military leader can not win a war against not very competent opponent with much greater resources. In the best case scenario Sweden could retain its territories on the Eastern coast of the Baltic Sea but this would require that the main opponent had a different set of the priorities (for example, being more interested in expansion into the CA, strengthening position on the Far East, concentrated on Wars with the Ottomans, etc.). In other words, maintaining of the status quo greatly depended on others policies. Chances are that Sweden would be losing pieces of land to Brandenburg even without the GNW.
Of course, it took a cool head to grasp situation fully and readjust policy accordingly. And the head cool enough to get that and intelligent enough to act upon that understanding was not available until 1810 (even if he was an elected nobody; well a nobody who managed to “made” himself is not quite a nobody).
Either Louisa look a more likely and better match for Peter in Sweden than Sophie.Um...am I the only one wondering why Karl Peter Ulrich would be married to Sophie of Anhalt-Zerbst? AIUI Fique was Yelizaveta Petrovna's choice for the reason that SHOULD she prove infertile or difficult to manage, that she could be sent home with the MINOR fuss.
OTOH, if by some time delay, KPU winds up as heir to Sweden instead of Russia (think there were only a few weeks between the two), the Swedish Estates are the ones who'll be deciding on his wife. And why would they go with anyone besides a Prussian princess for a nobody from Anhalt? (Luise Ulrike of Prussia's godmother was Ulrika Eleonora, Queen of Sweden, and there was an understanding that that Luise would marry Ulrika's son just as what Ulrika herself had previously been engaged to Luise's dad).
Likewise, Denmark had plans to marry Louisa of Denmark (OTL duchess of Hildburghausen) to whoever was chosen as heir to the throne of Sweden. It seems to me that BOTH Louises seem far more likely candidates than what Fique would be. (At least to me)