Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Add onion and celery and cook until soft and translucent, about 5 minutes. Turn off Saute function. Add chicken broth, garlic, soy sauce, rice vinegar, ginger, and pepper; stir to combine. Set frozen chicken on top and do not stir.
Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 4 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid. Stir to mix, then stir in sesame oil.
Select Saute function. Mix water and cornstarch together in a small bowl. Add to the bubbling liquid and stir until sauce has somewhat thickened, 3 to 4 minutes.