Thanks for the detailed explanation, I’ve never heard of “preferred sinks” or “preferred sources” until now. Much appreciated! 
My experience with the Wurkkos FC13 and my Xiaomi Redmi Note 9S aka Curtana running LineageOS was exactly the opposite: it works great (with the light charging the phone) unless the phone was under about 10% charge: then the phone starts paradoxically charging the light… 
Looks like someone (possibly the phone hardware or firmware developer, or the LineageOS folks) messed up. But at least it could easily been avoided by just not waiting for the phone to reach less than 10% charge before starting to recharge it (which is good practice re: extending its battery life anyway).
The sad thing about the X4S is, in its case it could have easily been avoided: as it needs “OTG mode” (ie powerbank / reverse charging) to be explicitly activated by putting the light in momentary mode, unless I’m missing something it would mean putting the USB port in “preferred source” mode, and avoiding the issue all together. That would have been a distinct improvement over the FC13, which just starts doing its thing (ie, direct or reverse charging) automatically a couple of seconds after plugged – would, because it seems it doesn’t actually work 
BTW, FFL calling its reverse charging / powerbank mode “OTG”: isn’t that actually a misnomer? AFAIK “OTG” in USB parlance means the data part of the connection operating both in “host” or “peripheral” mode, not the power part…