Hi Pete,
It sounds like the update may have interrupted the normal boot process, and the fact that the Surface shuts down before reaching Windows Recovery or UEFI suggests the issue could be occurring very early in startup.
I would first try a forced shutdown and restart: hold the Power button for about 20 seconds until the screen goes completely black, then release it and wait a few seconds before turning the device back on. If that does not help, try the Surface UEFI method again by holding the Volume Up button and then pressing and releasing the Power button while continuing to hold Volume Up for at least 15 seconds.
If the device still cannot enter UEFI or WinRE, the next step is typically to use a Surface Recovery Image from Microsoft on a USB drive. Since you do not currently have access to another USB-C device, you may need to borrow another Windows PC temporarily to create the recovery media.
The inability to access both Windows Recovery and UEFI is unusual, so if repeated attempts fail, it may indicate a firmware or hardware-related issue rather than a Windows-only problem.
Thank you, Pete, and feel free to respond back for more assistance. I can also walk you through the Surface-specific recovery steps and help determine whether this is a firmware or hardware issue.