Preheat oven to 425°.
Place squash cubes in a bowl and drizzle them with oil, stir well to coat. Place squash cubes on parchment paper on a baking sheet and sprinkle with salt and pepper. Roast until squash feels tender all the way through when poked with a paring knife, about 45 minutes. Allow to cool.
DO AHEAD TIP: Squash can be roasted 1 day ahead. Cover and chill.
Roast cut tomatoes at 400 degrees F for 30 minutes.
Heat remaining 1 tablespoon oil in your Instant Pot or a large heavy pot over medium heat. Add onion and saute until softened, about 5 minutes.
Make a well in the middle of the onions, add the garlic and stir for about a minute more.
Stir in 2 teaspoons salt and the turmeric. Cook until fragrant, about 30 seconds. Add roasted squash and stir to coat.
Add tomatoes, squeezing the pulp into the pot and discarding the skins.
Pour in chicken broth; bring to a low boil on the Saute setting. Reduce heat by setting the Instant Pot on Slow-Cook, High, add the thyme and simmer to allow flavors to meld, about 20 minutes.
Using an immersion blender, purée soup until smooth. (Alternatively, allow soup to cool slightly and purée in small batches in a blender.) Season with salt and pepper.
For a meat version, stir in shredded chicken. If you are serving the soup to both meat-eaters and vegetarians, place the bowl of shredded chicken on the side for self-serve.
If serving into individual bowls, garnish the “chicken” bowls with some chicken shreds and the vegetarian ones with thinly sliced heirloom tomatoes, then sprinkle with thyme sprigs.