I just tried to access my Azure account via Microsoft Edge and logged in fine but upon clicking on Portal was met with a fairly useless message

Clicking try again did nothing.

On searching the internet I found that if you press F12 in Edge to display the developer tools, the Cookies node had the following UE_Html5StorageExceeded.

Running localStorage.clear() from the developer tools console window is suggested here. Sadly this failed with an undefined response.

However Edge Crashing with HTML5 storage exceeded suggests going to Edge | Settings | Clear browsing data, clicking the button Choose what to clear and selecting Choose Cookies and saved website data followed by clicking the Clear button did work.

Oh and yes, sadly you will need to login again to various websites that you probably left logged in permanently.