References: Mini Powersupply
Li-Po charging IC, probably with 5V/USB charging
Pass through external power
Monitoring the battery status
A breadboard has 2 power rails, it would be nice to supply different voltages to both of them, so the first version could adjust from 0-24V. To keep it small a lithium battery could be used and two adjustable buck-boost converters with two voltmeters. Max 500mA-1A current is plenty.
Version 2 could have a negative rail, or an inverting buck boost power supply, also Ammeters.