Cut brisket in half to fit the multi-functional pressure cooker; place halves on a large plate or sheet of waxed paper. Season both sides of brisket halves with chili powder, oregano, onion powder, cumin, black pepper, herbes de Provence, and red chile pepper; dredge in masa harina, reserving any that falls off.

Turn on a multi-functional pressure cooker (such as Instant Pot) and select the Sauté function. Add oil until hot; add brisket and brown both sides of each half, about 7 minutes. Transfer brisket halves to a plate. Add onion, carrots, and celery; sauté until slightly softened, about 5 minutes.

Add chicken broth and beans to the cooker; add any reserved masa and browned brisket. Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 40 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 lid.

Remove brisket from the pressure cooker; set aside. Add potatoes, tomatoes, green chiles, and water to the cooker. Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 8 minutes. Allow 10 to 15 minutes for pressure to build. Trim excess fat from brisket and cut into bite-sized pieces.

Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove lid. Add up to 1 cup more water if too thick. Return brisket to the cooker; add garlic salt.

Cook on low heat until warmed through, up to 1 hour.