Not enough space to restore?

It is clear that the backup size on iCloud is greater than the total capacity of your new iPhone. You should overcome that if majority of the space in iCloud is used for Photos and Optimize iPhone Storage is set to ON on your new iPhone. That setting was also set to ON on your old iPhone during all the backups of it as well (according to you).

I am not sure whether the iTunes (PC method) method of restoring is accounting for iPhone storage optimization. It may be restoring the entire space (unoptimized) which is greater than the iPhone's capacity while when the space is optimized then it clearly fits within 128GB.

Can you ensure that Optimized iPhone Storage is set to ON on your old iPhone. Ensure that iCloud for Photos is set to ON. Ensure that iCloud for Messages is also set to ON. After that create a fresh back up on iCloud. Then attempt to restore your NEW iPhone with 128GB from iCloud instead of the PC. See whether that works.

Here is more information on this subject from Apple ➔ Move from your current iPhone to a lower capacity device.

Axel F.

Let's talk about your old phone.

Which method are you using to restore your new iPhone? Did you have Optimize iPhone Storage set to ON on your old iPhone? If you did then were you using iCloud for Photos? Messages etc? If you were using iCloud then how much storage space was used up in iCloud?

Axel F.