Does data from the apps migrate during data migration?

Maybe I didn’t explain properly. It is normal and expected behavior for the data from apps to transfer and then for the apps to download from the app store. That is exactly how it is intended to work. Your app data will transfer.

Make sure that you backup before you start to transfer the data to your new phone.

Transfer data from your previous iOS or iPadOS device to your new iPhone or iPad - Apple Support

My daughter recently purchased a new iPhone 14 at an Apple Store. The rep used Quick Start to transfer the data to her new phone from her old phone. Her apps started to download but the process did not finish until we got home and she was connected to our home WiFi network. It took about another 45 minutes until everything was completed.

Any data that is saved locally should move over to the new phone when you go through the data transfer process. Apps will have be to downloaded for the App Store again, but since your purchase history is data that is on your phone, the download will start automatically.

Any data that is synced with iCloud should also sync to the new phone. But data that syncs with iCloud is obviously not saved locally, it is stored in iCloud. Apps like contacts, notes, reminders, calendar events are examples of apps that can sync with iCloud.

No, it will not be removed. Data transfer is a bit of a misnomer. The data is actually copied to your new phone leaving everything on the old phone intact. What you are doing is cloning the new phone from the old phone.

After you set up the new phone, by using Quick Start, or restoring an iTunes or iCloud backup, the old phone will remain exactly as it is. All apps, data and settings will still be on the old phone.

You’re quite welcome. Enjoy your new phone.