Set the Instant Pot to Sauté and heat 1 tablespoon olive oil. Brown the diced chicken on all sides, then remove and set aside.
Add the remaining 1 tablespoon olive oil, then the onion and celery. Sauté 3–4 minutes until soft. Add the garlic and cook 30 seconds more.
Return the chicken to the pot. Add the broth, rice, salt, pepper, and bay leaves. Lock the lid, set the valve to Sealing, and cook on Manual/High Pressure for 8 minutes. Allow a 10-minute natural release, then quick-release the rest.
Remove the bay leaves. In a bowl, whisk the eggs with the lemon juice. Whisking constantly, slowly ladle in about 1 cup of hot broth to temper the eggs.
Stir the tempered egg-lemon mixture back into the pot (heat OFF or Keep Warm — do not boil). Shred or stir in the chicken, taste for salt and lemon, and serve topped with fresh herbs, lemon zest, and feta.