Heat a saute pan over medium-low heat. Cook chicken thighs in batches just until skin starts to brown, 2 to 3 minutes per side. Don't overcook; the meat should still be pink and raw on the inside. Set chicken aside in a bowl, reserving juices in the pan.

Saute onion and celery in the pan until turning translucent and browning at the edges, about 5 minutes. Transfer to a large bowl.

Add potatoes, rutabaga, turnips, carrots, mushrooms, and garlic to the onion-celery mixture. Sprinkle salt, herbes de Provence, onion powder, garlic powder, and pepper on top. Stir and mix vegetables until coated.

Place 1/2 of the vegetable mixture in a slow cooker. Add 1/2 of the chicken. Layer remaining vegetables and chicken on top. Pour vegetable broth over the mixture in the slow cooker.

Cook on Low for 7 hours, gently stirring every few hours if desired.

Use tongs to remove chicken from the stew. Let cool. Separate skin and bones from the meat and shred meat. Stir meat back into the slow cooker.