"dishes of any kind" and "any kind of dish" are similar or identical in meaning.
"kind of" is more common than "sort of" but they mean the same.
They should, by the rule, be followed by a singular noun, but this rule is not always followed.
Did you try hard? Well, I kind of tried..
Did you study for the test? Sort of.
Did you enjoy the movie? Kind of.
The general meaning is "yes, but not enough" or "yes, but not very much.
"kind of" and "sort of" are very, very, slang, and I'd expect to hear them mostly from young people.
I suggest you learn what they mean so you'll recognize them when you hear them.