@ImtiazAli 

OK, I tried again, as you have suggested, and it is still a no go.

To be absolutely certain that I am still missing the blindingly obvious, I have some questions:

Firstly, the utility, besides telling me "Couldn't find main Deco", goes on to say "Make sure you are connected to the Deco's network". The question is, what is the Deco's network, if it isn't the network named top right, in large letters, on the Network page of the Deco app?

Secondly, irrespective of whether I connect wirelessly, or via cable plugged in to the main Deco, the LAN scanner utility on the MacBook Air can see every device on the network - including the so-called main Deco - in great detail. So why can't the Deco M9 Plus Update Assistant?

Thirdly, FAQ-2930, Case two, proudly refers to PCs and Windows, and not Macs/MacBooks and macOS. So has the utility been tested on Apple Silicon devices like my MacBook Air and macOS Sonoma, given that the utility is dated March 2021, i.e. more than 3 years ago?

I await answers to each of my questions, and thank you, in advance, for your help with my problem.

  @ImtiazAli 

Network setup is as follows:

Cable broadband router connected to the internet. Router is not in modem mode, but wifi on router is turned off and main Deco is connected to the router via Ethernet cable. Never have been able to get modem mode to work, but this setup does. Quite obviously the main Deco is in Access point mode. Other than the main Deco - which is an M9 Plus - I have two other M9 Plus Deco devices, and most recently have added two XE75 Pro devices. So the front page of the Deco app shows the main Deco connected to the internet, and 4 Deco devices connected to the main Deco. It also shows 18 clients connected to the main Deco. There are no clients connected to the other Deco devices.

This setup seems to work OK, apart from not being able to update the M9 Plus firmware. The plan is to add in 3 XE75 Pro devices, make one XE75 Pro the main Deco, and then retire the M9 Plus devices. Doing it this way means I don't have to reconfigure the 18 clients.

However, as they say, the best laid plans of mice and men don't always go to plan. Hence for my need for your assistance, for which I thank you in advance.