ZF transmission fluid level check

Here's the relevant page from the manual of my ZF gearboxes.
Also mated to MAN engines, but much less powerful (V8/800), so definitely not the same model of yours, though I would expect the oil check procedure to be the same for most if not all ZF g/boxes.
If you're interested in something more specific, you must confirm the ZF model, because nobody can guess it from the engine type alone.

Neither 16L nor 16K are oil types I'm familiar with. I guess the classification is different between our sides of the ocean?
Anyway, attached is another page from my ZF manual, specifying SAE 30 (non-ATF) as generic oil type, plus some more detailed API and ACEA classes.
The page also includes a list of oil names, but that might well be outdated, since the manual is by now 20+ years old. The specifications still stand, anyway.
FWIW, the oil I always used is the Mobil Delvac 1330.

But again, as I said your ZF gearbox is bound to be completely different (larger) than mine, so while oil recommendations are likely to be the same, I can't be positive about that. I do have some other ZF manuals in my files, but if you want me to check if I've got yours, you should confirm the exact model - just take a pic of the plate attached to the gearbox, if unsure.

According to which manual?
If you check out the ZF manual page I posted, straight 30 is preferred, straight 40 is for hot climates, and multigrade oil is not even mentioned.

Same as mine, then.
Out of curiosity, do they call for either yearly or 500 hours replacement also in your manual?
Personally, I don't mind the 500 hours, but yearly replacement sounds pretty much like a CYA driven prescription, IMHO...

FWIW, here's the page of my manual mentioning either annual or 500 hours oil replacement interval.
They do mention also a one-off replacement after the first 50 hours, so good call from your part on that!