Iphone 16 is lagging right out of the box

It is expected that your phone will be slower, produce more heat and also drain the battery faster after it has first been set up. The phone is doing many background tasks that will be noticeable until it completes and includes:

• Analyzing all your photos for new object detection algorithms.
• Reindexing all the new files for spotlight searches
• Performing a large iCloud backup
• Building database for Siri Suggestions

This could take 3 days to complete and it is best to leave your phone plugged in whenever possible and especially every night. If you feel like there is an issue with touches not registering or the slowness has not resolved in the 3 days, then take the device back for a full refund. You have 14 days to refund your device when purchased at Apple or Authorized Apple Seller.

If you have not done a Force Restart yet, then you should do that as it is always a good idea to clean up cache files after a software update. It may take a couple of attempts to get the speed and sequence of the key presses correct and the last step of holding the side button until the Apple logo appears could take up to 15 seconds. Ignore anything else you see on the screen during that time.

Force restart iPhone - Apple Support