So a bit like how us Brits use "curry" then...
This is the problem. You borrowed a word that you don’t understand the depth of and are now arguing that it should be used in your way when people raise what it actually means. It’s a co-opting of a cultures word and cuisines.
There is no dish that’s “curry”. The British generalized it to be all spiced thick stews.
Would you call an eggs Benedict “a hollandaise”? Or roast potato’s as “chips”? No because there’s specifics to a dish that you afford it because you’re familiar with it. Calling them curries and expecting that to be the actual term is ignorance.
"Chips" is an interesting example to bring up, because the word means completely different preparations of potatoes in different parts of the Anglosphere...
And Hyderabad may have been politically separate. It’s not culturally separate. Unless you purposefully deny any migration.
Hyderabad is not some unique snowflake among the Indian diaspora.