Melt butter in a multi-functional pressure cooker (such as Instant Pot) set to the Sauté function. Add onion and sauté for 2 to 3 minutes. Add garlic and cook until fragrant, 1 to 2 minutes. Add mushrooms and sauté until starting to soften, 2 to 3 minutes. Cancel the Sauté function.

Stir in chicken broth, sherry, thyme, Worcestershire sauce, salt, and pepper. Close and lock the lid; select the Manual function and set the timer for 5 minutes. Allow 10 to 15 minutes for pressure to build.

Release the pressure using the natural-release method according to the manufacturer's instructions, about 10 minutes. Release remaining pressure carefully with the quick-release method, 2 to 3 minutes. Unlock and remove the lid.

Select the Sauté function again and bring soup to a light simmer.

Whisk flour into heavy cream in a small bowl; slowly pour into simmering soup, whisking constantly. Cook, whisking constantly, until thickened, 2 to 3 minutes. Cancel the Sauté function. Season with salt and pepper if needed.