Running our of storage on my iphone that still has over 50G of available space

You need iCloud storage to backup your phone. The message you paraphrased indicated that was the error message you had seen.

If you don't want to backup your phone to iCloud, then you can disable it and manually back up to a computer. This page shows you where to turn iCloud backup on/off: How to back up your iPhone or iPad with iCloud - Apple Support

If there's a different issue you'd like help with, please state it clearly.

~Lyssa

Using the phone's local device storage to back up other things in local device storage would not be terribly useful. In most circumstances where you would need the "local backup", you would have lost the ability to use the phone, and possibly even lost possession of the phone itself, rendering the "local backup" useless.

If you had to do a hard reset, and it wiped everything in flash (except Activation Lock), then it would be bye-bye to the "local backup" and bye-bye to restoring its data.

That is why you back up the phone to iCloud or to a Mac or PC.

If you're backing up to a Mac or PC, then you would presumably also want to keep backups of the drive that holds your iPhone backups.

That message means your iCloud storage, which is used to back up your phone, is too low. It has nothing to do with the storage on your phone.

~Lyssa