I precisely know what you're talking about, we have zillions of such landmarks too - they suffered during the WWII, and then during the communism, though, so vast majority of them is in way worse condition than this marvelous place.
I briefly asked the Brave AI, which generates responses based on web search:
The Czech Republic is known for its numerous castles and chateaux. While the exact number is debated, estimates range widely. According to some sources, there are around 2,000 castles and chateaux in the Czech Republic. Other sources suggest there could be as many as 3,000. The National Heritage Institute in the Czech Republic lists 932 castles as part of its heritage sites.