Thank you, that brought me on the right track. However, there are some weird things.
It turns out that the install_to command asked to repair the config file as there would be some unused entries. I acknowledged that. In the process, the smtp_host config was removed completely! I reinserted it, and it works. With or without the protocol prefix.
What's more, the documentation does not give a hint to add the protocol prefix. In the config.inc.php.sample this is not mentioned. I will continue to use that option without the prefix.