You could add a lot of things for the liquid of course. IMO I'd just add enough water to half way cover the already browned thighs. Put in a couple of sweet onions cut in halves, a few whole old tough carrots, a couple of large washed potatoes peeled. The potatoes will become the thickener. Enough veg to keep the thighs off the bottom. then set the turkey bits on these vegs. Add a bay leaf and couple of springs of fresh thyme, a few whole crushed pepper corns. No salt. No celery. No wine. Then low and slow until the turkey is falling off the bone. Remove the turkey bits. Now remove the thyme sprigs and the bay leaf. Now use a stick blender to puree the veg. 'Then 'finish' the puree with hot homo milk to which a nice amount of clarified butter has been whisked in. Then strain the sauce. Your sauce will taste bright and clean and like 'turkey' instead of apples or wine (beware! white wine when cooked for a long time will add a bitter note) or powdered salty bouillon cubes.
This is how I braise poultry. As in any excellent dish it's always the quality of the sauce that stands out.
I carefully debone the turkey bits trying to keep them as large as possible.
Creamy roasted garlic mashed potatoes with the turkey set on top with the sauce poured over. The big spoon full of cranberry sauce on the side. Don't forget the chopped fresh parsley lightly sprinkled to finish.
you could braise them with water, beer, wine, cider, fruit juice, stock -- pretty much anything that sounds good!
Milk wouldn't work well because it would curdle in extended cooking, but you could braise them in a little cider and then add a splash of milk or sour cream to make a creamy sauce.