It looks like Wi-Fi is the only way to do iCloud backup and restore. Is there any wired way to do this? I DO NOT HAVE WI-FI.

IN some cases an iCloud Backup can be done via 5G cellular data. See the following from Back up iPhone - Apple Support

Note: On models that support 5G, your carrier may give you the option to back up iPhone using your cellular network. Go to Settings > [your name] > iCloud > iCloud Backup, then turn on or off Backup Over Cellular.

The other option would be to backup to a computer via a wired connection rather than backing up to iCloud. See: How to back up your iPhone, iPad, and iPod touch - Apple Support

scaldcat wrote:

It looks like Wi-Fi is the only way to do iCloud backup and restore. Is there any wired way to do this? I DO NOT HAVE WI-FI.

Only way to do wired is using itunes/finder on a pc/mac, but that still requires wifi or network data.