Using the large holes of a spiralizer, cut zucchini into noodles, or cut zucchini into long noodles using a julienne peeler. Place zucchini in a colander in sink. Toss zucchini with 1 teaspoon salt. Let stand 20 minutes.
Heat oil in a large skillet over medium-high. Add tomatoes, oregano, and garlic; cook, stirring often, until tomatoes are wilted, 3 to 4 minutes. Remove mixture from pan; cool slightly.
Preheat oven to 375°F. Place half of zucchini noodles on a clean kitchen towel. Wrap towel around zucchini; twist and squeeze until all liquid is extracted. Repeat with remaining zucchini. Cut zucchini into manageable lengths.
Whisk eggs in a large bowl until lightly beaten. Whisk in milk, flour, pepper, and remaining 1/2 teaspoon salt. Add tomato mixture, cheeses, and zucchini; toss.
Wrap bottom plate of a 9-inch springform pan tightly with foil. Assemble pan; coat bottom and sides with cooking spray. Pour egg mixture into pan. Bake at 375°F until set in the middle, 50 minutes to 1 hour. Cool 10 to 15 minutes. Remove sides from pan; cut zucchini pie into 6 wedges.