I can't back up my iPhone

The backup is something that should be done while the device is fully functional to save yourself from situations such as one you are now in. If you iPhone doesn't work, you won't be able to backup the device. In other words anything on it is lost.

Having said that, unless you have deliberately decided to turn this feature off, when signed to iCloud on iPhone, the device does backup to iCloud automatically. In such case, all you have to do when the device is back from the service, you need to ensure to sign back to your iCloud account and on setup screen choose Restore Data from iCloud Backup.

https://support.apple.com/en-ie/guide/icloud/mm7e756df7fd/icloud