The Katholikentag attracts around 20,000 participants, spread over four days. There will certainly be more life in the city, but there won't be unbearable crowds at the sights, because the participants are coming for the program and not for tourist reasons. One advantage of the Katholikentag is that you don't have to rely on the usual two English tours per day for the residence, but can walk around freely and ask questions to the “Ciceroni” distributed throughout the building. What I could imagine is that the cathedral will be closed at times, but the most important thing about it is the building, not the interior (lost during the war). Incidentally, the main venue for the meeting, the Congress Center, is located far outside the city; this will draw some of the visitors away from the Altstadt. The restaurants of the large wineries will certainly be fully booked, but at least in the Bürgerspital there is a wine bar where you can taste and also buy wine (the entrance is on the corner of Theaterstraße and Semmelstraße). Add some snacks from the traditional Hanselmann bakery (Hofstrasse, directly opposite the Residenz) and enjoy them in the Hofgarten behind the Residenz, and your restaurant problem is solved.