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You don't have to use wi-fi to backup an iPhone - you can do it to a computer. If you connect the device to Finder on a Mac, or a PC with iTunes, you will be offered the update there.
Backups for 5G capable iPhones, from the iPhone 12 range or later, can use mobile phone data, provided that the plan has 5G capability and the carrier allows this.
For older - 4G or earlier - iPhones the data transfer is too slow and the connections sub-optimal for the important work of backing up your iPhone.
Apple is quite clear about the need to use wi-fi for iOS updates:
Update your iPhone, iPad, or iPod touch
- Back up your device using iCloud or your computer.
- Plug your device into power and connect to the internet with Wi-Fi.
- Go to Settings > General, then tap Software Update.
- If you see two software update options available, choose the one that you want to install.
- Tap Install Now. If you see Download and Install instead, tap it to download the update, enter your passcode, then tap Install Now.