Found it!
The value for DB_HOST in env.ini has to be the mysql container_name from docker-compose.yml which Docker then translates to the proper network address.
However, that did break my unit/feature tests tho'. And to make these function properly again - I had to make a copy of .env with a name .env.testing And in that file I changed APP_ENV=testing and DB_HOST=127.0.0.1
Duh :)