WAVGAT Pro Mini, no serial output
Okay, that was pretty fast. Something wrong with the board definitions/library? dunno. 

There are several implementations of the board definitions/library available and some are old or incomplete (?).

This version works and give you also some nice features as setting the clock speed and internal/external crystal etc. Take a look at:
https://github.com/dbuezas/lgt8fx

This one also works:
https://github.com/LGTMCU/Larduino_HSP

I have installed both and now the serial problem seems to be solved.
Additional info (of Ralph Bacon) can be found here:
https://github.com/RalphBacon/LGT8F328P-Arduino-Clone-Chip-ATMega328P



Warning:
However, I still don't know how stable these more feature rich clones are and how compatible these are with the Atmel/Microchip ATMEGA328P MCU. Time will tell, when I find some issues, I will update this answer.

Hopefully this info can help others too.