Initiate iCloud Backup on Disabled iPhone

Hello,

I broke my iPhone screen, which eventually started pressing buttons itself, until finally it entered the wrong passkey so many times that it disabled the phone.

I was away when I broke the screen, but the phone is set up on iCloud backup and I was hoping that when I returned home to a familiar WiFi network, it would create a new backup. But after a few days with the broken phone plugged in and connected to the WiFi, it has not initiated a new backup (though I can make it ring using the Find My app on a different device).

There is data stuck on the phone that I will only be able to access if it does a full backup. Since it is disabled, I can't connect it to a functional screen to retrieve anything.

Is there any way to tell the iPhone to run its automatic full iCloud backup? Or is there some reason why it hasn't already done that?

Thanks for your help