Place potatoes, broth, and 1 tablespoon salt into Instant Pot. Close lid, set pressure to high, and cook 20 minutes. Allow Instant Pot to remain on warm setting.
Meanwhile, in a large skillet over medium-high heat, warm olive oil and 1 tablespoon butter until melted. Add onions, season generously with salt, and cook, stirring occasionally, until deeply golden and caramelized, about 25 minutes. If necessary, add 1-2 tablespoons water to skillet to prevent burning, scraping bottom of pan to incorporate caramelization. Adjust heat as necessary to prevent burning.
In a small skillet, cook bacon over medium heat, stirring occasionally, until crisp. Remove with a slotted spoon to a paper towel-lined plate.
If necessary, release pressure manually on Instant Pot. Using an immersion blender, blend potatoes and broth until nearly smooth. Add milk, cream, and remaining 2 tablespoons butter. Blend to combine. Fold in half of cheese, half of caramelized onions, and thyme. Season to taste with salt and pepper. If soup is too thick, thin to desired consistency with additional milk.
Serve, garnished with reserved cheese, reserved onions, chives, sour cream, and bacon.