Is trasferring iPhone data after setup possible?

Yes, you can restore a backup and download all of your apps and app data, but if you do that, you will overwrite the current contents of your phone. If you have already backed up since you set up the phone, you may have overwritten the backup that you want to use.

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

You can download purchased apps again whether you restore a backup or not. The apps will no longer have the data associated with them, but some apps that sync their content with iCloud can access that data again but turning on the app switches in Settings>Your Name>iCloud>Apps using iCloud.

You can read more about downloading past purchases.

Redownload apps, music, movies, TV shows, and books - Apple Support

One option would be to start the setup over from scratch by first erasing your phone. See: How to erase your iPhone, iPad, or iPod touch - Apple Support

You can then use one of the following methods: Transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support

If you don't want to do that, you can install previously purchased apps on a new device; go to App Store, tap the circular user icon that is near the top right of the screen, tap "Purchased" and tap "Not on this device." Then download the desired apps. Note that it will no resinstall deleted data.