Heat oil in Instant Pot® on sauté. Add garlic and onion. Sauté until garlic is fragrant and onion is soft, about 5 minutes.
Add vinegar, basil, tomato paste, italian seasoning, and both cans of tomatoes. Lock lid. Set valve to sealing. Program for manual-high and 5 minutes. Use either quick release or natural pressure release when cook time ends. Stir in parsley.
Serve immediately or freeze in reclosable freezer bags or freezer-safe plastic containers that are instant-pot friendly, such as the ones in the NOTES below.
To use after freezing, remove from plastic container and add to instant pot with 1/2 cup water. Lock lid. Set valve to sealing, and program for manual-high and 0 minutes.