*** OK, this worked for a little while and then stopped. Sorry, thought this was a fix and it looks like NOT.
I tried and tried the different options here, nothing worked. Based on the ideas, I searched the New Outlook some more and found a solution that worked for me. Hope it works for others.
The idea was that Microsoft must have hidden the link options somewhere without telling anyone and then reset it or defaulted it to something that wasn't working for most people. I was able to find it on my system and it was not enabled.
I found it in Settings, General, Files and Links
Mine has two options, "Microsoft Edge" and "Default Browser"
Neither was selected and so I selected "Default Browser" and clicked save. BTW, after there was nothing selected still but I was able to click on links and they work now.
I hope this helps. Very annoying.