There is simply no technical reason or even excuse why external links have to be open in Edge. Messenger for Windows is the only app that I'm aware of that does this.
I use Firefox, and have used all its predecessors, going back to Netscape Navigator 2.0. I have also been a developer on some of its components for about a decade. I will not use a Chromium based browser, such as Chrome or Edge, unless the site absolutely won't work, but I will seek to use another site instead first.
The web version of FB messenger does not work correctly in Firefox. In particular, audio and video calls don't work in it. So, it's not a good solution. I believe abandoning FB Messenger altogether is the answer.
The good news is that just about everyone has a phone number, and there are plenty of other messaging apps that are not FB messenger. Even Meta's own Whatsapp client for Windows does not have this problem. Neither do Telegram or Signal messenger.
The problem that my mom would have with switching apps is that she talks to a fair number of people via Messenger, all of whom are old farts who barely understand how their current messaging works; they're not going to change to another unfamiliar app just because my mom wants them to. If it were feasible, I'd just get my mom set up on Discord, which I have open all day every day anyway, but that would leave her with just me to talk to. I suppose we'll just have to install Messenger as a web app and get used to it.