Place stew meat in a large bowl and season liberally with garlic salt and pepper. Add flour and toss to coat. Set floured meat aside.
Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Melt 1 tablespoon butter and add garlic. Saute until soft and fragrant, about 1 minute. Add remaining 1 tablespoon butter and floured meat; discard remaining flour in the bowl. Cook beef without stirring until browned on one side, 1 to 3 minutes. Stir and repeat until most sides are browned, 5 to 7 minutes more. Add beef broth. Close and lock the lid. Choose manual high pressure and set timer for 30 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer's instructions, 10 to 40 minutes. Unlock and remove the lid.
Add potatoes, carrots, and onion to the pot and stir to combine with beef. Close and lock the lid. Choose manual high pressure and set timer for 10 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.
Add Worcestershire sauce, coconut aminos, steak sauce, browning sauce, rosemary, and thyme to the pot and stir to combine. Taste and season with salt, if needed.