You can't rely on
any AS owner's manuals or schematics as gospel about where
your particular bath sink drains.
Only the full-scale-model testing reported here will work definitively.
With an empty grey tank, and its drain valve open, pour water down the bath sink drain. If water comes out the grey drain, you have your answer. If not -- with the trailer very quiet, and no water pressure, hold the toilet flush stopper open, and pour water down the bath sink drain. You should hear it falling into the black tank [which should be empty-ish]. This must be done without running the pump because it is too noisy.
You can
probably trust that the plumbing will not change configuration after this test, thus it need be done only once in the lifetime of your trailer.
PS -- If you can't perform the test above, these search results show other threads/posts on "sink drains into black tank" --
https://www.google.com/search?q=sink...=airforums.com