Your laptop is definitely able to run macOS 10.13 on bare metal. I was going to provide a link for the instructions to create a bootable macOS USB installer so you can install macOS to the external drive. Make sure to erase the whole physical external drive as GUID partition and MacOS Extended (Journaled). The installer will convert this volume to the APFS file system during the install process. Within Disk Utility you may need to click on "View" and select "Show All Devices" so that the physical drives appear on the left pane of Disk Utility. The physical drives will usually be identified by their make & model, but external drives may be identified by the USB controller of the drive, dock, or adapter being used to connect the USB drive. You would likely need the bootable macOS USB installer for all of the other options as well.
Create a bootable installer for macOS - Apple Support
Once you create the bootable macOS USB installer, you will want to reboot the laptop and hold down the Option key immediately after hearing the startup chime so you can perform an Option Boot to access the Apple boot picker menu where you can select the orange icon for the macoS USB installer.
After the first phase completes copying all of the installation files to the destination, the installer will reboot the Mac. In theory the installer should reboot to the external drive to complete the phase 2 of the installation process, but sometimes the Mac may instead reboot to the internal drive. Just reboot and do another Option Boot, disconnect the macOS USB installer stick, and select the remaining orange icon which should be the boot option for the external drive.
Once you have macOS 10.13 fully installed to the external USB drive, then you will most likely want to configure the default Startup Disk System Preferences to allow for your Big Sur drive to be the default drive to boot. When you want to boot from the external drive, just perform an Option Boot. You will need to click the padlock icon within the System Preferences in order to allow configuration of the Startup Disk settings.
While you are booted into macOS 10.13, macOS may tell you about a compatibility issue with your Big Sur drive. This is because Big Sur has a different drive layout from High Sierra. I believe it is due to the "Update" volume utilized by Big Sur which High Sierra does not understand. Also, macOS High Sierra won't see the Big Sur "Macintosh HD" volume correctly since there are actually two APFS volumes which Big Sur combines behind the scenes to make it appear like the older single "Macintosh HD" volume. The other Big Sur volume is "Macintosh HD - Data", the latter is where your Big Sur Users folder containing your data is located. To help avoid confusion, I suggest you give the external drive a unique name when erasing it with Disk Utility prior to installing macOS. Maybe name it "ExtHighSierra", or "ExternalSSD".
About the read-only system volume in macOS Catalina or later - Apple Support
Signed system volume security in iOS, iPadOS, and macOS - Apple Support
FYI, an advantage of using a VM is that you don't need to reboot the computer in order to access the other OS. However, a VM requires sharing CPU, memory, and storage with the host OS (Big Sur in your case). Parallels is probably the simplest VM solution for running macOS within a VM, although it is a paid third party app. Only the Parallels software needs to be installed. The OS running inside the VM will be stored in a virtual drive raw image file stored within the Big Sur file system which should never interact with Big Sur. The guest OS within the VM can be allowed to access the storage within Big Sur if you configure the VM to share a particular folder or drive for storage on Big Sur with the guest OS within the VM.
Good luck.