Can battery cause issues, even is connected to power supply?

I have my Muse Luxe always connected to power supply and I don’t really need battery. But I have heard that low battery voltage could cause stability issues (but it was unclear whether this applies to battery operation).

I am suffering from very bad instability and I also noted, that, despite always connected, the battery voltage/percentage follows cycles with voltage at a max and than reducing until it charges again. I also note that battery indicator always oscillates between 20% and 30%

Is this normal? Could this be the cause for issues?

And more importantly, is the ESP directly connected to the battery (like an “on-line UPS”) or bypassed when external supply is available (like a “line interactive UPS”) ?