In the Instant Pot, combine the broth, shrimp, mushrooms and their liquid, half the coconut milk, the ginger, chiles (if using), 1 tablespoon of the fish sauce, the lemongrass, honey, and salt.
Secure the lid on the pot. Close the pressure-release valve. Select MANUAL or PRESSURE COOK and set the pot at LOW pressure for 1 minute. At the end of the cooking time, quick release the pressure.
Stir in the remaining 1 tablespoon fish sauce, remaining coconut milk, the lime zest, and lime juice.
Divide the soup among four serving bowls. Garnish with cilantro and serve with lime wedges alongside for squeezing.