The process to transfer data from old to new iPhone/iPad is straightforward. Apps are not directly transferred between devices.
For Apps, if using the native transfer facilities, the transfer process creates a record of the Apps that are installed on the donor iPad - and it is this record of installed Apps that is transferred to the target (new) device. For Apps that are both compatible and available for download from the App Store, the corresponding Apps are automatically downloaded and installed from the App Store. If not using the native transfer or restore processes, Apps can be manually installed from the App Store. In all cases, you will need to be using the same Apple Account (previously known as your AppleID) - as, otherwise, Apps will have to be purchased again.
These support pages should get you started with setup of your new iPhone/iPad - and the methods of transferring your data from the source to target device:
Set up your iPhone, iPad or iPod touch – Apple Support
Transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support
Use Quick Start to transfer data to a new iPhone, iPad or iPod touch – Apple Support
If the donor iPhone/iPad, from which you are transferring your data precedes iOS 12.4, QuickStart will not be available.
“Transfer” is rather a misnomer. In reality, your data and setup is merely cloned to the new device. Nothing is moved or removed from the original device.
An alternative is to restore either an iCloud or iTunes backup to the new device:
How to back up your iPhone, iPad and iPod touch – Apple Support
Restore your iPhone, iPad, or iPod touch from a backup - Apple Support