protect standby lithium ion battery from continuous charge
You need a device called "micro UPS" - miniature Uninterruptable Power Supply. Or "Mini DC UPS". One of this kind (for DYI apps) is offered by Adafruit, kit #1944, 



see Mouser/Digikey/Arrow/whatever.

Or a device in a Rpi3 format:



CORRECTION: I withdraw my recommendation for Adafruit 1944 Kit. After examining their circuitry, I found that it doesn't manage the battery properly: when always on input supply AND having a load on 5V booster side, the Li-ion cell will be always subjected to charge voltage, and therefore will be overcharged eventually, resulting in bad batteries. Avoid this kit.