This may be due to the changes made in how Backlight uses Font Awesome. Matt has dropped Font Awesome 5 Pro and Backlight 5 now uses Font Awesome 5 Free and it loads locally rather than from the Font Awesome servers. See: Upcoming Changes to Font Awesome
What that may mean for Backlight 4 is that there is no longer access to Font Awesome 5 Pro and that could be breaking your icons.
I don’t remember if BL4 has the Settings option of serving Font Awesome locally. If so, you could use that and install the free version. I believe there is an info icon with that setting that tells you how.
You’d then need some custom css to make the free version work: Font Awesome 5 Free Unicode Fix - TTG Tips and Tricks
Another option is to simply update to Backlight 5