Some history about Firefox and BeOS. Before Firefox, there was Mozilla, which had a BeOS port (called Bezilla). Bezilla was bloated and slow. So the BeOS community tried to make a stripped version of Mozilla with only the browser (minus all the bloat). This project became an inspiration to do the same for Mozilla, and that product became Firebug (or something similar - edit phoenix, then firebird), which due to trade…
I see no mention of that on the Firefox Wikipedia page: https://en.wikipedia.org/wiki/Firefox#History.