Cut brisket in half to fit the pressure cooker. Place brisket on a large plate or sheet of waxed paper. Season both sides of each piece with chili powder, oregano, onion powder, cumin, black pepper, herbes de Provence, and red chile pepper. Dredge brisket pieces in masa harina; reserve any masa that falls off.
Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Add oil; when hot, add brisket to the pot and brown both sides of each piece, about 7 minutes. Transfer brisket to a plate. Add carrots, celery, and onion; saute until slightly softened, about 5 minutes more.
Pour chicken broth and beans into the pressure cooker. Add any reserved masa and the 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 and set aside. Add potatoes, tomatoes, green chiles, and water to the pot. 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 an additional cup of water if stew is too thick. Add brisket back to the pot. Add garlic salt.
Cook the stew on low heat until warmed through, up to 1 hour.