Turn on a multi-functional pressure cooker (such as Instant Pot(R)) and select Saute function. Heat oil in the pot. Saute onion until barely tender, about 3 minutes. Mix in Worcestershire sauce, garlic, beef base, pepper, thyme, and salt.
Pour in 1/4 cup vermouth; deglaze the pot by scraping the bottom with a wooden spoon. Add steaks; saute until browned, about 6 minutes. Turn off Saute mode. Add remaining vermouth, mushrooms, and 1 1/2 cups beef broth. Mix together gently.
Close and lock the lid. Select high pressure according to manufacturer's instructions; 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. Stir in noodles. Lock the lid and cook on high pressure until noodles are tender, about 3 minutes. Allow 5 to 10 minutes for pressure to build.
Pour remaining 1/2 cup beef broth into a microwave-safe bowl. Microwave until hot, about 1 minute. Dissolve flour in the broth.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Open lid and stir in the beef broth mixture. Let thicken, 3 to 5 minutes. Stir again. Add sour cream; stir until completely combined.