Scrape membranes from squash halves with a spoon, reserving seeds to roast, if desired.
Place steam rack, with handles in the up position, in the inner pot of a 6-quart Instant Pot; pour in 1 cup water. Place squash halves, cut sides up, on rack.
Close and lock the lid of the Instant Pot. Turn the steam release handle to “Sealing” position. Cook at High Pressure for 9 minutes. Open the cooker using Quick Pressure Release. Lift squash from the cooker using rack handles. Set aside on rack to cool.
While squash cools, pour out water from the inner pot; rinse with hot water, and dry thoroughly. Return pot to the cooker.
When squash is cool enough to handle, use a fork to remove spaghetti-like strands, and place in a bowl.
Add butter to inner pot. Press Sauté. When butter melts, add onion and garlic to pot; cook, stirring constantly, 2 minutes or until tender. Press Cancel to turn cooker off. Add squash strands to pot; stir 2 minutes or until thoroughly heated. Return squash to bowl; add Parmesan cheese and remaining ingredients, and toss well.