The error message "Verify volume failed: Unrecognized file system." means that Disk Utility couldn't verify your volume's file system. It may happen when your volume is corrupted or has partition table issues. This error can occur on both internal and external drives.
You can shut down your Mac and retry booting into the macOS partition. If that doesn't work, you can wipe your Mac partition and reinstall the operating system to fix the error.
Since your current Disk Utility version is outdated, it's recommended to reinstall macOS from a bootable external drive. If you have a T2 Mac, you can also try reviving or restoring your Mac using Apple Configurator.
Be reminded that this will delete all data on your Mac partition. So, you need to get your data off the partition first. To do this, you need to run Mac Data Recovery in Recovery Mode.
After your data is safe, you can create a macOS bootable installer and boot from it to format your Mac hard drive and reinstall macOS.