WRONG: URLs are still case insensitive, even for IDN.
CORRECTION:
The question was about IDN: "Are IDN domain names case-sensitive?"
My initial answer is wrong, and does not clearly answer the question.
It brings URLs into the mix.
The domain name part (IDN) of a URL is case-insensitive.
The other elements might be case-insensitive or not. It depends on many things, and in general is not predictable.
For instance the path part would normally depend on the OS or even the file system hosting the site (on MacOS you can format the drive as case insensitive or not)
But these days you can have some of these paths "hooked" to answer RESTfull APIs.
So it depends on how the "hook" is done.
Similar for other elements (user, password, parameters, parameter values)