The TalentCell item I posted a link to apparently has the same property; it has a 12V/6A input/output port which, so far as I can see, has to behave intelligently with regard to charging or supplying.
The standard way of doing this is with a 12V sealed lead acid (SLA) battery designed for the purpose; these things are charged with a constant voltage and happily supply the charge back when the voltage drops. These are what UPS’s use internally, as well as my gate opener; I bought the TalentCell to replace the SLA, but I haven’t tried it yet.
The word on the street is that keeping LiIon batteries around 100% charge, for example by charging them regularly even if they are still at 80%, does kill them. At least that is what my wife was told when she had to get her Samsung S8 battery replaced. These days I let the systems I have drop to below 25% before charging.
The LiPoly/LiIon BMS systems I’ve looked at recently are extremely misleading; they apparently have independent output and battery terminals, but the reviews on Amazon suggest those are simply connected together and there is no evidence of the required “boost” circuitry. Nevertheless so far as I understand it the charge circuitry is based solely on battery voltage, so it should be possible to run a load off it while charging. Doing it efficiently could be tricky, but if ravpower is doing it then there should be a cheap board out there.