Set Instant Pot to sauté, on normal if an option. Allow Instant Pot to heat up, then add the bacon. Stir the bacon every couple of minutes. After about 5 minutes, add 1/4 cup water to the Instant Pot. Continue to cook the bacon, stirring every couple of minutes allowing the water to cook off and the bacon to brown. In the last minute of the bacon cooking, add the garlic, stir until the garlic is fragrant.
Using a slotted spoon, removed the bacon and garlic onto a paper towel lined plate to drain. Use a ladle to remove as much of the bacon grease from the Instant Pot to save for later. Leaving a little bit of grease in the bottom of the Instant Pot is ok.
Break the spaghetti in half and add to the Instant Pot spreading it out and criss-crossing it so the pasta does not clump together. Drizzle in 1 to 1 1/2 tablespoons of the bacon grease over the pasta, making sure to reserve 1 tablespoon for later. Stir the pasta as much as possible, trying to coat the pasta in the grease. Add 4 cups of water to the Instant Pot. Cover and lock into place, sealing the release valve. Set to Pressure Cook on high for 6 minutes.
While the pasta cooks, add 1 tablespoon of the bacon grease to a small mixing bowl. Add 3 eggs, 1 egg yolk, the pepper and cheese to the bowl. Whisk together until smooth.
When the pasta is done cooking, release the pressure from the Instant Pot. When pressure is fully released, open the Instant Pot and stir in the egg-cheese mixture, bacon and garlic. Make sure to stir from the bottom to incorporate remaining starchy water.