iPhone can't restore from backup due to insufficient space

Today I noticed that all of my tables in my Notes app had been wiped and reduced to a single cell. Looking up this issue, I found that this is a common occurrence which is unfortunate.

I want to restore a backup from 7 months ago so that I can recover my Notes, but I am receiving the following message on iTunes:

""iTunes could not restore the iPhone because not enough free space is available on the iPhone"

I think when I made the backup, I was at around 63/64gb of my space. Am I getting this error because it will try to update my phone from 14.8 to the latest as part of restoration, and doesn't have enough space to do so?

I was able to extract my Notes from the backup using a third party app, but the important Note I need is password protected and I can't access the historical data...

I am now uploading 30gb of photos to iCloud to free space, but will that do anything? It's still failing with around 10gb free of space on the phone. Any tips are greatly appreciated. Thanks!