How can I attempt to resolve a kernel panic error without data loss?

The first step is a forced restart. Press and hold both the power button and volume down button simultaneously for about 10-15 seconds until the Apple logo appears. If that doesn't work, try connecting the iPhone to a computer and attempting a restore through iTunes or Finder (macOS Catalina and later). Backups are crucial before attempting a restore, but if you haven't backed up, the risk of data loss is present.