Combine cranberries, orange juice, water, cinnamon stick, and vanilla extract in a multi-functional pressure cooker (such as Instant Pot). Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 1 minute. Allow about 10 minutes for pressure to build. As soon as the cooking cycle finishes, turn the Instant Pot off to avoid overcooking.

Release pressure using the natural-release method according to manufacturer's instructions, about 7 minutes. Unlock and carefully remove the lid.

Turn Instant Pot back on and select Sauté function. Stir white sugar and brown sugar into cranberry mixture until sugar melts. Season with a pinch of salt. As soon as sugar has melted, turn off the Instant Pot to avoid overcooking.