Add the vegetable stock, wild rice, mushrooms, garlic, carrots, celery, sweet potato, onion, bay leaf, and Old Bay seasoning to the bowl of an Instant Pot.
Stir briefly to distribute the ingredients evenly.
Secure the lid and cook on manual/high pressure for 25 minutes.
When cooking is complete, allow the pressure to naturally release for 10 minutes. Carefully open the vent to release any remaining pressure.
Remove the lid and carefully discard the bay leaf.
Stir in the coconut milk and chopped kale. Allow the kale to soften in the hot soup for a few minutes.
Taste the One Pot Wild Rice Soup and season with salt and freshly cracked black pepper as needed.
Ladle into bowls and serve warm.