Thanks for answering. Just doing some quick looking into it myself beyond what you mentioned in your answer. In the French Wikipedia article it mentions that Napoleon Bonaparte learned of her existence in 1802 when he overheard a conversion about her and then brought her to Paris and there was some jealously from the Empress and her daughter since the Emperor became very fond of her (although jealousy among the Emperor's relations both blood and in-laws seems pretty par for the course).
Also Eugène de Beauharnais's eldest daughter marries Crown Prince of Sweden (only son of former French Marshal Bernadotte and Napoleon Bonaparte's dejected fiancée Désirée Clary) while her own eldest daughter marries deposed Swedish Crown Prince in exile in Vienna.
Also Queen Sophie of the Netherlands mentioning her death in her correspondence google<dot>com/books/edition/A_Stranger_in_The_Hague/rp29cF15SpAC?hl=en&gbpv=1&dq=Duchess%20Hamilton%20inauthor%3AQueen%20Sophie%20(consort%20of%20William%20III%2C%20King%20of%20the%20Netherlands)&pg=PA206&printsec=frontcover
First of all: thank you so much! I feel like poor Stéphanie really is overlooked, because she did not stay at Napoleon's court for long. Basically, she gets noticed by the First Consul (or possibly rather by Josephine), sent to Madame Campan's bording school (because where else) and only truly shows up at court in 1805/6, in order to be married off to poor Karl von Baden, who had just lost his former fiancée Auguste von Bayern to a certain Eugène de Beauharnais (Stéphanie's cousin).
Which is a story in itself, of course.
I am not sure the cousins were particularly close. In a letter to Eugène Josephine refers to Stéphanie as "la petite Beauharnais", the little Beauharnais, which seems a bit odd given the close family relations. But it also could just be a nickname and need not mean much.
The marriage to Karl von Baden - as the story goes - started out exceptionally bad. By most accounts, Karl was not a friendly character in the first place, and he was still hurt about having been denied a good marriage (to a princess from an old regime princely family) and now being ... strongly invited to conduct a - in his eyes - bad one with some lower nobility girl who had merely been adopted by the French emperor. (According to Bavarian crown prince Ludwig, Karl shortly before his marriage accused Ludwig of not having done enough to strengthen his sister's resolve and to avoid Auguste's marriage to Eugène de Beauharnais.)
Stéphanie, as to her, was not yet 17 years old and obviously not enchanted to get married to this strange German. When Karl showed up in Paris for the wedding, he still wore his hair braided in the Prussian fashion, much to the horror of his Parisian teen bride, who declared this hairstyle, and with it the bridegroom as a whole, inacceptable. When Karl went to see a barber and returned fashionably coiffed à la Titus - Stéphanie started crying and declared he was even uglier now.
As I said, not a good start. And it did not get much better because - as the story goes - during her wedding night Stéphanie locked herself up in the bedroom with some friends from bording school, while Karl was left outside, passing the night on a chair in front of the bedroom door... allegedly.
While much of this may be exaggeration and court gossip, there's little doubt that the marriage was not a happy one. During the Prussian campaign in 1806 Napoleon even felt the need to write to the marshal in whose corps Karl von Baden was to serve, in order to make sure that Karl would not get mocked openly by the soldiers. And I remember one letter to Berthier in which Napoleon wrote something to the effect of "Okay, if he absolutely wants to come, let him join the army. But I really wish he'd go home and make a baby with his wife!"
Poor Stéphanie must have felt quite alone in that rather strange Baden family she had married into. The person actually calling the shots in Karlsruhe was Amalie von Baden, Karl's mother (and also the mother of Queen Friederike of Sweden, Queen Karoline of Bavaria and the Tsarina Elisabeth of Russia). Karl's grandfather, Grand Duke Karl sen., was old and increasingly senile, but he had a young second wife in what was called a "left-hand marriage", and this lady was in a permanent feud with Amalie. Lastly, the old grand duke also had another son, a known intriguer and womanizer.
Happy family times. Especially as all these illustrious personalities immediately united in their dislike of that second class French princess they had been forced to accept into their family.
And it seems Stéphanie, after trying to adapt to her new circumstances, rebelled quite a bit. Enough to earn her some stern rebukes from her imperial adoptive father.
It took until 1809 for the situation to truly change, until Josephine had to leave court and the Beauharnais and their foreign relations thus lost their closest link to the French court. Napoleon's marriage to an Austrian may have been felt as a threat by all of the smaller Rhinebund states, who had received French support mostly in order to serve as a buffer against Austria, and who now suddenly found themselves sandwiched between two - always hungry - super powers. Their princely families immediately closed ranks, and this included Stéphanie.
Or maybe Karl had really started to grow fond of his wife. Their first daughter was born in 1811. And after Napoleon's fall, Karl refused to try and get a divorce. (It did not keep him from heaving wild orgies during his stay at the Vienna Congress though.)
Stéphanie did end her life in Baden, where she was very well-liked by the population.