2013 Mac Pro and

Hi Anthony Stough1

That machine is now long out of support by Apple however you can still find some information in this archived document:

About EFI and SMC firmware updates for Intel-based Mac computers – Apple Support (UK)

You will still find some of the firmware updates on this Apple website although I know that several have been deprecated:

Apple - Support - Downloads

On the webpage type in the search box "Mac Pro Firmware" should return you a list of the available patches.

HTH

Will.

What is current macOS version?

Do you have an Apple SSD installed?

An Apple SSD is required since the Monterey upgrade includes a firmware update to the Mac. The Monterey installer need to write to an Apple disk so the firmware can be updated. If no Apple disk the Monterey install terminates with various error messages.

Also, if you have an AppleSSD there was one instance in either this forum or the MOnterey forum where the users got that error when skipping macOS versions and going directly to Monterey. If They resolved it by going to the intermediate macOS versions before finally going to Monterey. You can get other Mac OS version here:

How to get old versions of macOS - Apple Support

In the past Mac firmware updates were separate updates but for many years they have only been part of macOS upgrades and even update to macOS version.