Quick start won’t activate after iOS updated on new phone

I was in the process of transferring from an iPhone 12 Pro to a 14 Pro using quick start. Part way through it said that the new iPhones iOS needed updating - so I waited for that to happen. Once it was updated, the phone just set up as normal but didn’t transfer anything across from my old phone. I am connected to internet/wifi and power with Bluetooth turned on and have restarted both phones but cannot get quick start to display again. I can’t transfer from iCloud or iTunes as I don’t have enough storage space to backup my whole phone. How can I get quick start to work?