Connecting power cable to device without enabled power supply = battery low?
Devices with DC jacks and internal batteries typically contain a switch in the jack that redirects power when the plug is inserted.

When a de-energized plug is inserted into the jack, you've activated the switch and reconfigured the circuit. In the absence of external energy, the battery is still powering the circuit, but in a different configuration. If the external supply voltage is higher than nominal battery voltage, perhaps the "full battery" level changes when the plug is inserted. That would mean that the "decrease" in battery voltage isn't happening at all, and the device is telling you whether the external supply is within expected limits. When the jack is removed, "full battery" level decreases and you see an apparent increase in battery voltage. Have you checked the user manual?

Try measuring voltage across the batteries with and without the plug inserted. You can trust a voltmeter much more than you can trust the software in your consumer electronics.

Smartphones don't do this because it is not how they are designed. The behavior you've witnessed is the result of how those devices are designed.