Peel all 3 lbs (1.36 kg) of russet potatoes and cut them into uniform 1-inch (2.5 cm) cubes. Even sizing ensures they cook at the same rate — larger chunks stay more intact while smaller pieces help thicken the broth.
Dice the yellow onion into small ¼-inch (6 mm) pieces and mince the 4 garlic cloves finely. Set both aside until ready to add to the slow cooker.
Add the cubed potatoes, diced onion, and minced garlic to the slow cooker, then pour in the chicken broth and the undiluted condensed cream of chicken soup. Sprinkle in the salt, black pepper, garlic powder, and onion powder, and stir everything together to distribute the seasonings evenly.
Cover and cook on LOW for 6–7 hours or on HIGH for 3.5–4 hours, until the potatoes are fork-tender and slide off easily. Avoid lifting the lid during cooking, as this extends the cook time by 15–20 minutes each time.
About 30 minutes before serving, add the softened cream cheese (cut into small cubes) to the slow cooker and stir well. Replace the lid and continue cooking on LOW for 20–30 minutes, stirring once or twice, until fully melted and incorporated.
For a chunkier soup, mash some potatoes against the side of the slow cooker with the back of a spoon; for a creamier texture, use an immersion blender to partially blend about one-third of the soup directly in the insert. Do not fully blend — leave plenty of potato chunks for texture.
Switch the slow cooker to WARM, stir in the 1 cup (240 ml) of sour cream until fully combined, then taste and adjust salt, pepper, or garlic powder as needed.
Ladle the hot soup into bowls and top each serving with shredded cheddar cheese, a dollop of sour cream, crumbled bacon, sliced green onions, and fresh chives as desired. Serve immediately with crusty bread or biscuits.