In a small mixing bowl toss salmon chunks with chili crisp. Set aside.
Heat olive oil in a Dutch oven over medium heat. When oil is hot, add onion and summer squash and cook for 3-4 minutes, stirring occasionally, until starting to soften.
Add garlic and rosemary or sage and cook briefly until fragrant. Add chicken stock or water, Kosher salt, and pepper.
Cover and reduce heat to low. Cook for about 20 minutes or until squash is very tender and browned on the bottom. It will begin to smell nutty and caramelized when ready.
Meanwhile, place a large covered pot with a couple inches of salted water over high heat.
When water boils, cook pasta per package directions for al dente. Reserve ½ cup pasta water. Drain and return pasta to the pot.
When squash is done cooking, remove lid and add lemon juice. Stir and scrap any bits stuck to the bottom of the pan. Transfer contents of the pot to a blender or food processor. Set aside.
Wipe out Dutch oven if needed and place over medium-low heat. Add salmon along with chili crisp. Cook 2-3 minutes per side, or until lightly browned and it flakes easily with a fork.
While salmon is cooking, add ¼ cup of pasta water to the squash mixture and blend until fairly smooth. Add more pasta water as needed if the sauce seems too thick.
Add squash sauce to pasta and toss to coat. Divide into bowls and top with salmon, feta cheese, and fresh herbs.