Interesting. I just use the precompiled package for broadcom-wl. But it’s not available for rt kernel. Have you tried installing broadcom-wl-dkms through pamac (Add/Remove Software)?
Or run the command
pamac install broadcom-wl-dkms
After that, try rebooting your system 1-3 times. And finally, just wait 5 mins for it to load properly. If it’s still not working, don’t hesitate to reply here again.