Moving to lower capacity device, storage now full, but iCloud isn't. Can't fully restore--solution?

Pretty much this exact post: Switch from a 256GB iPhone to a 128GB one… - Apple Community

but here is the question: why can't I just push everything that just won't fit to the iCloud instead? For context, I buy 2TB of iCloud storage, and it isn't anywhere near full.

Seems that I'm in a bit of a conundrum. Moving from 256 iPhone X to 128GB iPhone 12 pro max and now the storage is full on the new phone. Ok...no problem...just keep the excess to the iCloud right? But the phone/iCloud arent doing that.

I read the support page here: Move from your current iPhone, iPad, or iPod touch to a lower capacity device - Apple Support but I don't have a computer to back things up to and MIL is stubborn on not deleting anything. Is she hosed?

Lastly, is there anyway to stop the restoration process and just keep the excess on the iCloud? Problem is that as things are removed, more data is pushed from the iCloud, but I need that storage space to recieve texts/emails.