Place pork roast in a slow cooker; season with garlic powder, poultry seasoning, salt, and black pepper. Add broth, 3 stalks celery, quartered onion, and apple.
Cover slow cooker. Cook on Low until very tender, about 8 hours. Transfer pork roast to a large platter. Discard juice and vegetables. Shred pork roast with a fork; return to slow cooker.
While pork roast is cooking, melt butter in a large saucepan.
Add 2 cups chopped celery and 1 1/2 cups chopped onion; cook until onion is translucent, about 5 minutes.
Add ketchup, water, vinegar, brown sugar, Worcestershire sauce, mustard, liquid smoke, and garlic powder.
Reduce heat to low; simmer, stirring occasionally, until sauce is thickened, about 10 minutes.
Pour barbecue sauce over shredded pork.
Cover slow cooker. Cook on Low until flavors combine, about 2 hours more.
Awesome Pulled Pork BBQ · Dinner Match Lab | Dinner Match Lab