Apps did not transfer to new iPhone

That is correct.

Apps do not transfer from an old iPhone. Instead, they are re-downloaded from the cloud to the new iPhone. So you must have your new iPhone capable of receiving downloads - well charged, connected to Wi-Fi (or 5G cellular with an appropriate plan), etc.

Apple apps don't need to transfer as they are already on your new iPhone. As sberman has eluded to the non-Apple apps will take some time to download from the Apple Store ... or you will have to manually download apps that you got outside of the store from their respective sources.

As far as app data, this too will take a bit of time. Some of it will come from iCloud sync, some from backups, etc.

Well, some apps download slower than others. They don’t all download in the same instant.