how to stop edge from being managed by an organization

Check whether you have OOSHUTUP installed.

OK - Rahul - I've just downloaded and run it, what should I be looking for?

Did you fix it?

Sorry, that was not what I meant. If you have O&OSHUTUP installed and have made changes to the Edge browser using this utility, you'll notice the "Your browser is being managed by your organization" message. If you disable all modifications made with the utility, the message should disappear, indicating that your system isn't compromised by malware or a virus. I should have clarified this earlier. However, if you see the message before installing the utility, it's advisable to follow the fixes/solutions mentioned in this thread, as there's a strong possibility your system has been infected with malware/virus—unless you're using an enterprise version of Windows or have added a work/school account to Edge. If you're unable to identify the issue, I recommend performing a fresh installation of Windows, which should resolve the problem.

How to do a clean install of the windows 10:

Windows 10 Clean Install Guide | The ENTIRE process | How to Install Windows 10 - YouTube

How to do a clean install of the windows 11:

Windows 11 Clean Install Guide | The ENTIRE process | How to Install Windows 11 - YouTube

For mass installation of all the necessary apps you can use this utility from github: https://github.com/ChrisTitusTech/winutil 

You can see it's usage and features from YouTube

Thanks for the detailed response, Rahul!

My version of Office 365 is a "school/work edition" and that's the problem, I realise, as it is also responsible for blocking the new VPN option within Edge. But, since that allows me life-long access to 365 updates, I'm living with it, for now!

Not yet - see my reply to Rahul!