Rub the smoked paprika, garlic powder, onion powder, and salt on the chuck roast.
Place the chuck roast in a 4- to 6-quart slow cooker.
In a small bowl, combine the ketchup and apple cider vinegar. Spread the ketchup over the roast. Add the water around the roast. Cover and cook on LOW for 8 hours.
Remove the roast from the slow cooker and transfer to a cutting board. With 2 forks or a shredder, shred the meat.
While the meat is cooking, in a bowl, add the cabbage, carrot, and avocado oil mayonnaise and stir to combine.
Refrigerate for at least 10 minutes.
Stack the meat slices on a romaine lettuce bun and top with the coleslaw.
Serve with cucumber and red onion slices, if desired.