When you use Quick Start, it doesn't necessarily reduce the size of the apps or their data. Instead, it attempts to transfer the entire app along with its data to the new device. The apps are re-downloaded from the App Store, but the data associated with those apps, such as user preferences, login information, and in-app content, are transferred.
The size of the apps themselves is largely dependent on the versions available on the App Store. If there have been updates to the apps since your last download, the newer versions may be downloaded during the transfer process.
Regarding storage and cache, Quick Start aims to bring over app data, including caches, to maintain a seamless transition between devices. However, the exact behavior can vary depending on the app and how it manages data. Some apps may still need to re-download certain content or update their cache after the initial transfer.