Turn on a multi-functional pressure cooker (such as Instant Pot) and select Sauté function. Heat olive oil in the pot; add celery, carrot, onion, and garlic. Cook, stirring occasionally, until onion is translucent, about 5 minutes. Turn off Sauté mode.

Stir chicken broth, beans, paprika, and thyme into vegetables in the pot. Close and lock the lid; move the valve to Sealing. Select high pressure according to manufacturer's instructions; set the timer for 34 minutes. Allow 10 to 15 minutes for pressure to build.

Select Cancel/Keep Warm when cooking is done. Release pressure for 10 minutes using the natural-release method according to manufacturer's instructions. Move the valve to Venting and release remaining pressure using the quick-release method, about 5 minutes.

Unlock and remove the lid; stir ham and tomatoes into bean mixture. Close and lock the lid; move the valve to Sealing. Select high pressure according to manufacturer's instructions; set the timer for 7 minutes. Allow 10 to 15 minutes for pressure to build.

Release pressure carefully using the quick-release method, about 5 minutes. Season soup with salt and pepper.