Select SAUTÉ setting on a programmable pressure multicooker (such as Instant Pot). (Times, instructions, and settings may vary according to cooker brand or model.) SelectHIGH temperature setting, and allow to preheat 2 to  3 minutes. Add butter to cooker, and cook until melted, about 1 minute. Sprinkle with flour, and stir to combine. Add russet potatoes and stock. Press CANCEL.

Cover cooker with lid, and lock in place. Turn steam release handle to SEALING position. Select MANUAL/PRESSURE COOK setting. Select HIGH pressure for 5 minutes. (It will take 15 to 20 minutes for cooker to come up to pressure before cooking begins.)

Carefully turn steam release handle to VENTING position, and let steam fully escape (float valve will drop). (This will take 1 to 2 minutes.) Remove lid from cooker. Mash russet potatoes with a potato masher until partially mashed. Add Yukon Gold potatoes. Cover cooker with lid, and lock in place. Turn steam release handle to SEALING position. Select MANUAL/PRESSURE COOK setting. Select HIGH pressure for 5 minutes. (It will take 10 to 15 minutes to come to pressure before cooking begins.)

Carefully turn steam release handle to VENTING position, and let steam fully escape (float valve will drop). (This will take 1 to 2 minutes.) Remove lid from cooker, and stir in whipping cream, salt, and pepper. Divide soup evenly among 4 bowls, and top evenly with bacon, cheese, and chives.