I'm studying lithium cells and their related mainstream modules.
One of the most common -yet wrong- use of the TP4056 module is to use it with the USB 5V input and an active load on the output (at the same time). AFAIK this will screw up the charge ending trigger current.
What if I add a diode, from the USB +5V to the load's positive, and a Schottky diode from output+ to the load's positive? I'll lose efficiency due to the (small) diodes' voltage drop but this is acceptable to me.
When the USB is connected the load will see the USB 5V, minus the diode's voltage drop, and, provided that the USB source is big enough, it will also charge the cell. Without the USB connected the load will be powered by the TP4056 in its standard configuration, except for the small Schottky voltage drop.
With the USB connected there isn't power consumption from the cell to the load during the charge process, because of the diode, and therefore also the terminating current can be properly trigger and stop the charge.
Am I missing something? Provided that I'll add a dc-dc step up converter, it's within the TP4056 specs to be used in this contraption as a 5V UPS for a device that only consume a few (3) watts?