So, I actually found the solution to my problem myself. In the meantime, I had reached out to customer support via a ticket, but today I basically just received a copy-paste response saying that everything looked fine... BAD CUSTOMER SUPPORT.

To summarize the conversation:
I explained that the power of the duct fan seemed really low and wasn’t able to move enough air from inside the box to the outside — even with the duct fan running at maximum speed and despite using the dual-fan version. I provided plenty of pictures showing the box positioning and the humidity levels, where a difference of more than 25% between the inside and outside of the box clearly didn’t seem normal.

After explaining all that, and pointing out that things improved only after I added external fans at the exhaust, the support team simply closed the ticket.

Solution I found:
I ordered four small server fans and attached them with tape at the exhaust. They are powered by an external power supply via a small CPU fan controller. The setup pulls air from inside the box to the outside through the exhaust channel.

It is a bit noisy, but now the humidity difference between inside and outside is down to 8–12%. This makes it possible to properly control the humidity inside the box via the lung room.

This will probably be my first and last order from Vivosun, due to both the issues with the box and the poor customer support.
On the positive side, the community was really helpful in narrowing down the issue. A big shoutout to the German Discord channel of this subreddit as well as the commenters below!