Turn on a multi-functional pressure cooker (such as an Instant Pot), and select Saute function on normal setting according to manufacturer's instructions.

Mix oregano, thyme, paprika, salt, and pepper in a small bowl. Season chicken with spice blend.

Heat 1 tablespoon butter and olive oil in the pressure cooker until butter is melted. Quickly brown chicken on all sides, about 3 minutes. Remove chicken.

Add onion and cook until translucent, about 2 minutes. Add garlic and cook until fragrant, about 30 seconds. Remove onion and garlic from the pot.

Melt a second tablespoon of butter in the pot, add rice, and stir constantly until fully coated and toasted, about 3 minutes.

Pour in wine and scrape up any browned bits from the bottom with a wooden spoon. Cook until wine is absorbed and alcohol cooks off, about 2 minutes.

Add chicken stock, chicken, and onion mixture to the pot; mix until well combined. Turn off Saute function.

Close and lock the lid. Select high pressure according to manufacturer's instructions, and set timer for 5 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.