Chicken holds so much water in my experience, especially the thighs.
But your question was how to safely 'hold' pre-browned chicken to braise later, closer to mealtime. I'm surprised it makes such a mess on your stovetop. A foil barrier or a higher sided pot like a dutch oven helps with that. I no longer brown meat. I brown at the end of a braise uncovered in my oven at a higher heat the last 1/2 hour 45 min. I'm guessing you just want that chore of browning out of the way. If that is the case, line the browned chicken parts onto a wire rake lined sheet pan, single layer, and into the fridge. Uncovered.
Issues some have is no fridge space. My high shelf holds nuts, seeds, dried fruit. One down is a bottle rack that holds seltzer bottles that can be removed.
Crispy skin is dry skin. Why I give time in the fridge uncovered with a dry brine rub. I never, or would consider, pre-browning a whole chicken and still get very crispy skin by giving it some time uncovered in the fridge. 6-8 hours or overnight. A bit of softened compound butter under the skin even better.
2 hours is a long braise for chicken but your recipe might be using a lower temp.
