The task manager icon does indeed correctly turn orange.
Default web browser is set properly. I tried setting it to Chromium and every single app I tested with Chromium, correctly opened and took focus with Chromium. Switched back to Firefox and once again it's not always taking focus. Only this time, when I tested Steam, Firefox didn't take focus from Steam even though it did before.
This definitely seems to be an issue with Firefox + Wayland given that Chromium had no issues opening up all the links from different apps I tried.
At least the issue is now whittled down a bit more. Thanks for your help!