I had the same issue upgrading from an iPhone Xs (256GB) to iPhone 13(256GB). The phone to phone transfer never works for me. I also recall the phone to phone transfer didn't work several years ago when I upgraded to the Xs. The storage on my Xs was not even half used. The Xs backup file was 2GB. With this 13 upgrade, the phone was immediately useable but I waited 9 days for it to wrapup the download. The error message fluctuated from 100MB needed to 500MB needed despite 199GB free storage space (and backup only 2GB). I called apple tech support and spent hours on the phone trying to restore and fix the issue. It became clear that everything was backed up on the phone correctly but the restore failed to resolve and shutdown. We verified this by connecting the 13 to my macbook pro and we could sync, change music, etc. Efforts to try to shutdown the backup failed and the lockup prevented us from turning off the icloud account. So after many hours we decided to restore the iphone 13 with no data transfer from the icloud backup. First we verified that all of the 3rd parts app data was already being stored on the iCloud. Then we did factory reset back to a basic app phone. Once you sign into your icloud account, it restores your basic email, calendar, contacts, notes. Once you enter App Store click on your picture icon (top right) , click on purchased (apps) and toggle between "All" and "Not on this Phone" to choose all of the apps that you want to redownload. I found my data within the 3rd party apps was restored. I hope this helps.