In the stopped state the STM8L needs just a few µA - but in this state the console can't wake up the device: the USART gets no clock. Only GPIO interrupts and peripherals that are clocked from the LSI or the LSE will work! A possible solution is a pin-change interrupt on RxD for waking the core - and the USART - up. In "Active-Halt" mode RTC and WUT peripherals run on 38kHz LSI or 32.768kHz LSE clock (see here). This means that it's possible to have a background task without keeping the core busy.
One of the challenges ist that STM8L docs doesn't describe the USART behavior if the clock is turned on after the start-bit edge, i.e., if the character that wakes the core from "Active-Halt" can still be received.