Set the Instant Pot to sauté mode. Add the oil and butter, and let it heat for about 2 minutes. Add the garlic paste, red onion, and parsley; cook for 3 minutes, stirring often to prevent burning. Then, add the white wine, salt, pepper, and chili flakes. Stir and let the contents heat for about 3 minutes. Finally, add the shrimp to the pot. Cook until the shrimp is opaque and curled to a "c" shape. This should take about 5 minutes. When the shrimp is cooked, remove it from the pot with a slotted spoon, leaving the juices behind. Place the shrimp in a separate bowl and set aside.
Add the seafood stock and lemon juice to the pot. Bring to a gently simmer and deglaze the pot, scraping pieces from the bottom with a spatula or wooden spoon. Break the pasta in half and place into the pot, separating them as much as possible with tongs and making sure they are completely covered with liquid. Do not stir after this point.
Place the cover on the pot, secure it, set the nozzle to "sealing", and set the timer to 2 minutes (*see notes) on high pressure (pressure cook setting). It will take the IP about 6 minutes to build up pressure before it begins to cook.
Once the pressure cooker is done and starts to release steam, carefully turn the nozzle to "venting"
Remove the lid from the Instant Pot. Add the shrimp, halved tomatoes, arugula, lemon zest, and pecorino romano. Stir to combine and let it sit for 5 minutes before serving. Garnish servings with extra chili flakes if desired.