I received the 18650 "UPS" module from Aliexpress, and have been testing it. Below are pictures and the schematic. The module includes the battery holder, a micro-USB input port, the standard TP4056-type charger, a single-chip battery protection circuit, a load sharing circuit, and an MT3608-type boost converter. It works as a USB, with no minimum stay-alive current, and no dropout when the charging source is connected or disconnected. It does not have a Type-A USB port on the output, just holes that you solder leads to.
As delivered, the module doesn't work. That's deliberate. There is no connection between the charging circuit and the boost circuit. The seller recommends that you mount a switch (not provided) in the two through-holes provided for that, or just deposit a solder blob on two pads. Apparently they think most users will adopt the solder alternative so the output is always on. But that means the only way to disconnect the battery from the boost converter (which has significant idle current) is to remove the battery, which is not what you want to be doing. Since the through holes are 0.1 inch apart, I installed two male header pins, and make the connection with a jumper block when needed.
I ordered the 5V output version, which they confirmed, but they actually sent me the 12V version. So I had to remove the 200K resistor R8 and replace it with a 75K resistor. It's probably best to order from a seller that sells only the 5V version - less likely to get the wrong one.
I found that the operation of the boost converter messed up the charger chip. It would not complete charging the battery. With 5v input, and the battery at 4.06V, the red charging LED was on, but no charge current was being provided. When I disconnected the boost circuit, charging completed normally. I suspected that pulses through the inductor were feeding back to the charger Vcc and causing it to malfunction. As the schematic shows, there was no capacitance in the circuit anywhere on that line, either at the charger's input or at the converter's input. So I added a .22uF film capacitor at the input to the charger, and that fixed it. I don't know what the appropriate capacitor would be for this circuit, but the one I added worked well enough, even when drawing 1A at the output, which is the nominal maximum load. But I suspect it should ideally be a lot higher value, and possibly one capacitor for each chip.
One unusual item in this circuit is the protection chip, the FM5056. It's a single chip that combines the functions of the more familiar DW01 with its companion dual N-channel mosfets. I have not tested the protection functions. As a reminder, you probably should use an unprotected battery in this module. It will still work with two protection circuits, but that just draws more idle current, and doubles RDSon.
The load sharing circuit is what makes this module particularly useful. With it, the external power source powers the boost converter directly when present, and the battery can also be charged independently if needed, with no load current to confuse the charger. The absence of a Type-A USB connector at the output is a disappointment, but this "UPS" is a better solution for powering projects than a power bank, and the price is certainly reasonable. I would just like to get some clarification on the needed capacitor if any experts would like to offer an opinion.