Ladies and Gentlemen, Gents and Gentesses, Dudes and Dudettes,
Kodi v18 changed the default scraper for TV shows from “TheTVDB” to “TheMovieDB”. (Obviously, I have gone through all those menus so often that I can blindly walk through them without noticing that the scraper changed.) I still have no clue why TheMovieDB scraper wouldn’t pick up my Tatort TV show, but I installed the TVDB scraper, configured it, used it as scraper for TV shows, and voilá – my Tatort shows are in Kodi! 
Edit: TheMovieDB uses a different naming scheme, s01e01 instead of s1970e01 (for the Tatort show). That’s why the TheMovieDB scraper couldn’t pick up the episodes and disregarded them silently. Luckily, the TheTVDB scraper is still available for installation. Otherwise I’d have to rename a couple thousand episodes (or, at least, a couple hundred Tatort episodes).
So far, thanks for your support!