Well it's a question of ROI. How many Linux users are there really that can't wait to install Microsoft software on their desktops? People who use Linux as their desktop operating system are probably using open source alternatives of any MS client software.

And for Office they would use browser version which works fine. It makes no sense for MS to invest resources into this since there isn't enough interest to justify the investment.

“Refuse” is a fairly strong word and suggests there is a Linux version available and just withheld. Software and features don't just appear out of nowhere.

Indeed. Not to mention that Office Online works just fine in a browser under Linux.

This assumes there are Linux users that actually want to use the Edge browser though

I know what you mean. For Edge there's probably not many folks who would be interested, but Office, for one, is still something that's desirable for a lot of folks who use Linux just because of numerous compatibility issues with LibreOffice.

It's a lot easier to just run Office in Wine. It's been a few years, but the last time I tried, that worked.

Honestly, if they were going to have a Linux client at this point, I would expect it to just be an Electron wrapper around the Office 365 webapps.

Wine does not run Office 2016.

Which flavour?

With flatpaks and Appimages these days, you don't really need to target any distro anymore.