Is the laptop battery stressed when it is connected to the mains?

En
1

There are only 3 scenarios right?

Laptop runs on battery → battery discharged
Laptop is being charged → Laptop is running on power adapter and battery is charging slowly
The battery is full, the laptop runs in its own circuit directly from the power supply unit, i.e. There's no current through the battery unless the charging cable is unplugged.

have I understood that correctly?

At

Yeah, okay… At point 3 there are two variants…

Either the battery is full and the supply to the battery is switched off, or a trickle charge voltage remains. This then prevents the self-discharge that every battery has.