Her husband died in 1907 and this could be the date of this photo, but the (red?) cross on her sleeves suggests this could be a war time photo.
The photography studio, Schuhmann & Sohn GMBH, is still in business a century later.
From eBay; monocolor tint removed. Also posted to her Subalbum here.
Princess Luise is dressed in widows dress, quite possibly with a tight skirt suggesting war time instead of 1907.
Keywords: Schuhmann & Sohn, Luise of Prussia, Luise von Preußen, Prinzessin Luise Marie Elisabeth von Preußen, Grossherzogin von Baden, Princess Louise of Prussia, Prinzessin von Preußen, Luise Marie Elisabeth, Princess, Grand Duchess, Hohenzollern family, Zähringen family German, straight coiffure, attifet headdress, veil, collar, lace capelet, necklace, long close sleeves, contrasting cuffs, close over-skirt, widow’s dress