Make the kimchi-skyr: In a large saute pan set to medium heat, add olive oil. Stir in onion, garlic, 2 tablespoons of kimchi, and a pinch of salt and pepper. Saute for 8 minutes on medium heat, stirring occasionally and lowering the heat as necessary to prevent any burning, until onions are soft and translucent. Reduce the heat to medium-low and cook for an additional 6 to 8 minutes until the onions are golden-brown on the edges. Remove from heat and transfer to a bowl; set aside and let cool to room temperature.
Pan-sear the mushrooms: Meanwhile, prepare the mushrooms. Wipe the same saute pan clean, then add canola oil on medium-high heat. When hot, add the mushrooms in batches to prevent any overcrowding in the pan. Sear the mushrooms for 3 to 5 minutes until nicely browned. Larger mushrooms will take longer, while smaller mushrooms will cook more quickly. Resist the urge to flip them early to allow them to fully sear. Once browned, reduce the heat to medium, flip the mushrooms, and cook on the other side. Season with salt and pepper. Remove from the heat and let cool slightly until warm but not hot. Repeat with the remaining batches, adding more oil if needed.
Assemble the dish: Stir in 1 cup skyr into the bowl with the onion/garlic/kimchi mixture. Mix in 1 tablespoon of the reserved chopped kimchi, and season with salt, pepper, and a pinch of garlic powder. Arrange skyr on a serving plate, and top with warm mushrooms, herbs, and garnish with the last tablespoon of kimchi.