Hello, Joe, there are unfortunately conflicting informations in the Apple documentation.
The Apple Watch User Guide, that you quoted, says "Mac (2013 or later) ", but the Apple Support Document
Automatically unlock your Mac with your Apple Watch - Apple Support
says more precisely "Mid-2013 or newer Mac using macOS Sierra", which is leaving out the early 2013 Macs, probably because the missing Bluetooth 4.0. There have been quite a few user posting here, who could not get this feature to work on early 2023 Macs.
If you have a direct line to the team writing the user guides and support documents, could you please ask them to update and resolve the conflicting items in the documentation " early 2013 Macs versus 2013 Macs"?
Regards
Léonie