Combine mango, apples, sugar, vinegar, ginger, sea salt, paprika, chili flakes, cinnamon, cardamom, cloves, pepper, and bay leaf in a multi-functional pressure cooker (such as Instant Pot(R)). Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 12 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure carefully using the slow-release method according to manufacturer's instructions, about 10 minutes. Release remaining pressure using the quick-release method, about 5 minutes. Unlock and remove the lid. Select Saute function; cook until chutney has thickened, about 10 minutes.
Let cool completely before storing in sterilized jars.