Shred zucchini with the shredding blade of a food processor and toss with 1/2 teaspoon salt in a colander. Let the zucchini drain for 2 to 3 hours if possible. Transfer zucchini to several layers of paper towels and squeeze out as much liquid as possible.
Heat olive oil in a large skillet over medium-high heat; cook and stir garlic with 1/2 teaspoon salt and black pepper until garlic is fragrant, about 1 minute. Stir in portobello mushrooms and cook until mushrooms have released their liquid, the juice has evaporated, and the mushrooms are browned, about 15 minutes. Stir shredded zucchini into the mushrooms and cook, stirring often, until the zucchini are tender but not mushy, about 5 minutes.
Bring a large pot of lightly salted water to a boil; cook the linguine at a boil until tender yet firm to the bite, about 11 minutes; drain. Transfer linguine into a large serving bowl.
Toss pasta with zucchini-mushroom mixture, Parmesan cheese, and mushroom Alfredo sauce, tossing until thoroughly combined.
