In a small food processor, finely chop the trout. Transfer to a bowl. Using a spatula, fold in the yogurt, crème fraîche, herbs, lemon zest and juice, and capers. Season with salt and pepper.
Spoon the mixture into a pastry bag fitted with a plain round tip. Pipe the dip into 10 small glass jars or ramekins. Cover and refrigerate for at least 1 hour. The dip can be made up to 1 day in advance.
When ready to serve, garnish with microgreens and serve with bread sticks and raw vegetables.