And I generally mix it with some sauce and it might sit in there for some minutes. So the cooking process actually continues after you remove it from the water. Cooking a bit longer in the sauce and shorter in the water is going to help the flavor and texture. There's no point in being hyper precise about the cooking time and then letting it sit for five minutes or whatever in the sauce. Nobody ever measures that time. Add pasta water to loosen the sauce if it absorbs too much.
Speaking of pasta water, use less water for boiling paste; not more. Many TV cooks get this completely wrong. They'll dump 100 grams of pasta in a gallon of water. Complete waste of time, energy, and salt (assuming they season the water correctly).
Especially if you plan to use the starchy water for your sauce, you need to use as little water as you can get away with. If you use too much water, there's not going to be a lot of starch in there. If it still looks like clear water by the time your pasta is cooked, you used way too much water. You might as well just use tap water for your sauce. The water should be cloudy not clear. As long as it doesn't cook dry, it's fine. About 2-3x the dry weight should be plenty for most pasta types. Restaurants tend to reuse their pasta water for multiple batches of pasta so they'll use more water. But the water has lots of starch after a few batches.