Pasta water does help to thicken the pasta sauce.
So when you drain the water from the pasta you should leave at least a half cup of water in the pasta and then add your pasta sauce to the pasta.
The pasta water is starchy and salty which helps to act like a glue for the pasta sauce so that it sticks to the pasta much better.
Cooking pasta in the sauce is not recommended as it makes the sauce get absorbed more into the pasta.
You should cook the pasta first, then drain the pasta and add the pasta sauce while the pasta is still warm or hot which makes the pasta sauce stick to the pasta much better.
Jarred Pasta sauce is already cooked and ready to eat.
All you have to do is pour the Jarred Pasta Sauce onto the Pasta when ready and it's good to go.
Although I do like to heat the Jarred Pasta Sauce up first and then add the heated pasta sauce to the pasta.
But you don't need to cook the Jarred Pasta Sauce because it's ready to serve and eat.
When adding pasta sauce to the pasta it's best to pour the warm pasta sauce onto the pasta while the pasta is still hot.
And toss the pasta around in the sauce in the pan to mix the pasta sauce in with the pasta.
You don't want to cook the pasta in a cold pasta sauce as it can absorb too much of the pasta sauce and make it come out bad.