A workaround for this is to 'Install Facebook' through the Chrome browser. In Chrome, navigate to https://www.facebook.com/messages/ and in the URL bar on the right-hand side there will be an icon of a screen with a downward facing arrow. Hover over that icon and it should say 'Install Facebook'.
This will install Messenger as a Google Chrome app and allow you to open links in Chrome instead of being forced to use Edge given the recent changes.