The TP4056 cards are normally preset for 1A charge and 10% cutoff or 100 mA. The reason it is bad to charge while using, is the current is only sensed on the charger output not the battery alone.
If the load took most of the 100 mA cutoff, the charger would never cut off and the battery's cycle rate of 500 or less would be cut according the time spent with the charger on > 3.9V.
So adding 5 mA load means the cutoff is now 95 mA which is OK.
If the load were 50 mA, I would want the cutoff to be 4.1V but it's pre-fixed.
For the longest lifespan/ charge cycles, battery University reports using the capacity between 25% and 75% is best. But if you reduce the CV voltage from 4.2 towards 3.9V you will lose some mAh capacity this way, but can get 10 times total mAhr life usage out of it.