'Update' volume appeared after High Sierra install

Solution 1:

Note: This answer assumes the reader does not have a Fusion drive.

When selecting the Erase button on the top of the Disk Utility window, you should see a popup window similar to the one shown below.

If instead you see a popup window is similar to the one shown below, then you are not erasing the entire drive. If the drive is not visible on the left side of the Disk Utility window, then press the key combination ⌘2 to show all devices.

When erasing the entire drive, you should select APFS for the format and GUID Partition Map as the scheme, as shown below. (Although, if you chose Mac OS Extended (Journaled), then the macOS installer would automatically convert to APFS.)

From the way I read your question, I do not think you erased the entire drive. You would probably be better off starting over and erasing the entire drive. This should eliminate the Update volume.

Also, consider this: Big Sur uses a newer version of APFS than is known to previous versions of macOS. So if the APFS container was created or updated by Big Sur and all you did is erase a volume before installing High Sierra, then the verify and repair software included with High Sierra may not function properly. So if you need to verify or repair APFS, you should first boot to a Big Sur version of macOS recovery. This is why you would be better off starting over and use the Disk Utility that came with the High Sierra installer to erase the entire drive.