Place the steam rack inside a multi-functional pressure cooker (such as Instant Pot). Add water to the pot. Place spaghetti squash onto the rack. Close and lock the lid. Select high pressure and set timer for 10 minutes. Allow 10 to 15 minutes for pressure to build. Release pressure using the natural-release method according to manufacturer's instructions, 10 to 40 minutes. Scrape squash into a bowl, separating into strings.
While squash is cooking, heat oil in a large skillet over high heat. Add onion and thyme and saute until onions are soft, 3 to 5 minutes. Add mushrooms, garlic salt, and black pepper; saute until mushrooms have released their liquid and are tender, 3 to 5 minutes more. Add pine nuts and cook until toasted, about 2 more minutes.
Add cooked spaghetti squash to the skillet with the mushroom mixture. Season with additional garlic salt and black pepper to taste. Cook for 1 minute more. Remove thyme sprigs before serving.