Sonoma refusing to shut down -- and a successful solution
Simply this: upgrading to the next OS: Sequoia 15.4 -- solved the issue.
I see many others indicate this issue and in the conversations rarely is a solution working for the questioner; and it is a frustrating issue.
And unlike other OS upgrades there was not too much that was different to learn and all the settings, etc. from Sonoma were maintained in Sequoia. It happened with ease on my M2 MacAir 2022.
And I tried everything else suggested - safe mode reboot; diagnostics; recovery (in face i paid to have this by an Apple technician as I did not want to, again, change the OS; because it was too technical for me to accomplish). The technician said it was a 99% chance that it was a hardware problem (which would have been expensive to resolve, most likely with buying a new computer!)
I hope this is of assistance to others experiencing this issue.
If there is a more appropriate way to post this kind of 'sharing a success' message I'd be glad to be informed about it.
MacBook Air, macOS 15.4