new messenger opens links in EDGE instead of default browser.

I tried an older version of the app and it didn't show the popup with the option for "not now," leaving me only able to upgrade or close the app.

That's strange, assuming your version is the same as mine (mine is 2150.23.211.0, downloaded from the link I shared - you can check your version in Windows Settings > Apps > Installed Apps > Messenger > [three dots] Advanced Options). Mine does try to scare me by saying, "Update by [some date] to continue using the app." But the date keeps changing to either the day the popup appears or slightly in the future, and it's an idle threat - the rest of the popup doesn't change and I can always click "Not now" and use the app as is. Here is a screenshot of the popup it gave me right now.

Yeah, mine used to look like that, complete with the date continuing to push further out, but not anymore, it just has the button to update Messenger.

At this point my problem with using it as a web app or just having messenger.com open is that there's no indication of new messages, either on the tab or the taskbar. It's really annoying.

This isn't so much of a Microsoft issue but more of a Meta decision. They knowingly went this route. How absurd.

I'm pretty sure that it was Microsoft who offered them big money to put their new version of messenger on Edge browser. We know what a dirty player is Microsoft when it comes to such things. We know all their tricks. I don't even have a doubt that this was all Microsoft's idea to do this.

They are no longer allowing you to use the old app. Got the notice today that if I want to continue to use messenger on my pc, I have to download the new edge app

The icon also disappeared for me. I'm guessing it happened with the latest update done today. After many hours of searching, I did find a way to do it. In Chrome, click on the 3 dots at the right, click Cast, Save & Share, then Install Page as App.

Save https://www.facebook.com/messages as a bookmark and use that in Chrome instead of an app in windows. Messenger is now a webapp, just launch it from Chrome instead of a button on your toolbar.