Why my new iPhone 16 app icons are greyed out and showing as waiting?

That is because when you are transferring your data over to your new iPhone, your apps are not saved in your backup, only sometimes the data is, meaning they must be reinstalled to your device. This in large numbers can take a while, so as Mac Jim ID stated and I will add on to quicken the process, make sure your iPhone has a strong Wi-Fi connection and is plugged in.

Restart your phone and make sure you have a solid internet connection.

Assuming that you have a good strong Internet connection, it is still going to take time for everything to appear on your iPhone.

Try to limit your other activity for the next few hours.

Check back in 4 hours to get a read on the progress of things.