Yeah, I’m not aware of any test aimed at Japanese learners that contains composition questions.
There’s another test, called the J-Test, which I’ve talked about before and am taking again this weekend, that contains sections that require writing. But they are merely kanji reading and grammar questions that don’t have multiple choices. They don’t test you on how well you compose Japanese.
There are tests with composition that you can take, but they’re all for natives, that I know of.