Is project size the size of finished App?

Hello i am almost finished my first game! But I am wondering if the size of my project with all the library files is going to be the size of the finished app on the actual Apple App store?

No

You can get a rough number by setting the build to IOS Device then going up to the top bar and clicking product and selecting archive. After it finishes it should popup with the details and you can click on Estimate Size. Most of the size is going to be from resources, so if you need to shrink it down that is the place to look.