Why do I need to delete files from a half-empty iphone in order to sync?

That message is telling you the computer does not have enough free space for the iPhone backup.

You need to keep at least 20GB+ of free space available at all times for the normal operation of the computer. If you completely run out of space on the computer with an APFS file system, then bad things will likely happen with the computer. If this happens, then it may be impossible to delete any files from the computer to free up space which will then require erasing the computer followed by reinstalling macOS & restoring from a backup. Erasing a computer will destroy all data on the computer.

I see iCloud in the background beneath the error message. How much free storage space do you have on your iCloud? The default free iCloud storage space with your AppleID is just 5GB.