You managed to get Linux running on your USB stick, but when you try to use it with Windows, it jumps straight to Windows. It seems like the setup or compatibility might be an issue. Have you checked the USB driver installation or tried a different USB port? Also, ensure your system is updated and that the USB device is recognized properly.
You didn't specify the file system type, so I assumed it was formatted correctly. Otherwise, it might not boot in the Surface Book.
Only a single volume exists, though the one containing the / mount point uses ext4, while another has fat32. I think the volume with the / mount point is indeed ext4 and the other is fat32, and the mount point for that fat32 partition is likely /USB_NAME.
The system fails to start on the main drive. Be aware, this software is from Microsoft and any non-native options are prohibited. All storage must be formatted as FAT32.
If the system uses UEFI, choose NTFS. For older BIOS setups, stick with FAT32. When both are supported, NTFS works best.