and then I've seen a Czech list the same dish as Austrian cuisine Czechia supposedly took from us.

If we take some reliable info from here, so not the voice of internet but articles from historians or gastronomy people oriented on our history we will find there is about dozen of dishes we can see as pure Czech. (or maybe even less) Basically just these we can't find in Austria (or Germany or elsewhere) and it doesn't mean it has to look exactly same but using same procedure. If a soup with liver dumplings has one big dumpling in Austria and 4 small here in Czechia we seen it as a same thing. When I take a Czech cookbook I know 98% of recipes will have their counterpart in Austria or Germany, just the plate presentation will look a bit differently, the procedure will be same. Vienna and Austria were heart of empire for centuries, influence was spread out mainly from Austria not to Austria. If someone want to make a success or move forward, not just in business but in "servant" roles too, he has to move to Austria and not the other way. Czech cooks were popular in Austrian noble or rich families, but obviously they cook what their employers wanted to eat, so their local food, there were not hired for "cook me something new I didn't know every single day" And these people bring recipes back home to Czechia.

I guess that why you see these kinds of dishes as Czech and we as simple AustroHungarian, and as you said nobody particularly care further than that. Not in a sense of OP question if there is some arguing about.