Combine Sauce in Pot: In the Instant Pot insert, whisk together soy sauce, water, vinegar, ginger, garlic, and sugar. Add white pepper.
Add Chicken and Veggies: Add the chicken, onion, and mushrooms to the pot. (If you prefer very tender zucchini, add it now. For firmer zucchini, see notes.)
Pressure Cook: Secure the lid, set valve to SEALING. Pressure Cook on HIGH for 3 minutes. The pot will take 7-10 minutes to come to pressure.
Quick Release: When the program ends, immediately perform a quick release of the steam. Carefully remove the lid.
Thicken Sauce (Optional Step for Best Texture): Use a slotted spoon to transfer chicken and vegetables to a plate. Press SAUTÉ. When sauce simmers, slowly whisk in the cornstarch slurry. Cook for 1-2 minutes until thickened.
Add Zucchini (if using firmer method): Add raw zucchini to the thickened sauce, stir to coat, cover (with pot off), and let steam for 3-5 minutes until tender crisp. Return chicken and other vegetables to the pot and stir to combine.
Serve: Serve hot over rice, garnished with green onions and sesame seeds.