I think we FINALLY nailed that bug.
The issue was caused by doing the following
1. Close all browsers (prior to opening the game)
2. Open Bitburner
3. Open a link from inside Bitburner.
4. Close Bitburner
At that point Steam considers the browser to be part of bitburner because bitburner opened it.
What the game now does it relegates URL opening to the OS instead of directly opening the default browser.