I had the same issue with my new IPhone 15 Pro yesterday and was able to set up today successfully by following these steps (keep in mind I use windows PC)
1- Set up your phone without restoring data from cloud or another phone (3rd option)
2-Sign into your ID and access your phone
3- Open ITunes from PC, make sure iTunes has latest Update
4- Connect your new phone to laptop/PC to connect to ITunes
5- After IPhone is identified in ITunes it will either ask you to automatically update to new IOS or you will have to manually choose it from setting (it works either way)
6- After download is completed, it will automatically install it on your phone (it took me 40 min to complete, upgrade size was 8GB and my connection was slow)
7- After new IOS is successfully downloaded on your phone, make sure to check it from general, software update (it will state your phone has latest version)
8- Sign out of apple ID
9- Go to General, transfer or reset phone
10-Erase all content and settings and confirm
11- IPhone will restart again and restart the process of setting up the phone
12- choose the option of transferring data from your other iPhone or restore from cloud (I chose to transfer from my old iPhone)
That’s it.. it will transfer data successfully and not ask for IOS update again
TIPS..
1- If you have already downloaded the software and it’s stuck, make sure to delete it from iPhone storage before starting this process
2- If your download is painfully slow (2 or 3 hours) then reset network settings! It worked for me straight away
Good luck.