What causes the butter to leak from the crust while baking?

You should need to knead (har har) at all - with a butter crust you really just want it to come together. I suspect that you needed to chill / rest the dough longer. Pie crust loves cold. I always make my pie crust dough the day before and fridge it over night, then roll it and put it in the pie plate and re-chill, then fill and bake. With this recipe I might try forming the crust then chilling it again before filling and baking it. Also, you night try having a baking sheet in the oven already hot. Form the galette on parchment paper on a sheet or a cutting board or whatever then slide it from that surface to the already hot one in the oven.