About 1 hour before cooking, salt the pork all over and let it rest on a rack set in a rimmed baking dish.
In a small bowl, make the sauce: Stir together chicken stock, sesame oil, tamari, chili garlic sauce, and xanthan gum. Set aside.
When ready to cook, press the “Sauté” feature on the Instant Pot. Add half the oil to the pot and wait for the display to read “Hot.” Sear the pork tenderloin in the pot for 2 minutes on each side. Remove the pork to a plate.
To the hot pot, add the remaining olive oil. When hot, add the ginger and garlic and cook, stirring, for about 1 minute. Add the mushrooms, stir, and cook for 2 minutes. Tuck the seared pork into the mushrooms and pour the sauce over everything. Close the lid and turn the valve to seal. Press the “Manual” or “Pressure Cooker” button, depending on your model, and set the cook time to 5 minutes. Use High Pressure default.
Once the 5-minute cooking time is done, allow a Natural Pressure Release for 20 minutes. If the pot is still under pressure after 20 minutes, do a Quick Release. Open the lid and remove the pork to a plate from the pot to rest for a few minutes.
With the mushroom sauce still in the pot, press the “Sauté” feature and allow the mixture to come to a vigorous simmer. Cook, stirring often, until the mixture has reduced to a glossy, thickened sauce, 3 to 4 minutes.
Slice the rested pork, arrange it on a platter or individual dinner plates and top it with the mushroom gravy. Garnish with the green onion and sesame seeds and serve.