@Vincent-TP concerning the current firmware:

I've not tried updating to 1.3.3, as that specifically states that it's only updatable from 1.3.2 according to the firmware page:

The error message is unspecific:

I can access the corresponding AP, and the controller can, too:

I'm rather stumped what to do here. Thanks for getting back to me!

  @Vincent-TP this (i.e., custom upload) is how I convinced the system to upgrade to 1.3.2 (it offered me 1.3.4 out of the box). I'll try 1.3.3 now.

  @Vincent-TP yes, port 8043 is open for myself (that's how I made the screenshots of the Omada controller) and also open for the devices to connect to the controller. The controller can also connect to the APs, and vice versa, even though that has to happen through a firewall. Possibly, I've found the culprit: it seems that the Omada Controller does not have enough stack space and fails to serve the file. I've restarted the controller with -Xmx2048m, and now it seems that it upgrades fine to 1.3.2 for one device. I'll try the others.

Yes, this seems to have done the trick, the updates ran through after fixing the Java heap size of the controller. It's rather unfortunate that the controller does not show any information except in server.log that the heap is full, and that the default heap size isn't automatically set to a larger value than the OS default (Debian presumably sets this to 256M I guess). Okay, so that should resolve this issue!