After some more digging I finally found a way to get my certificate tab back. You have to manually set a few values in the MySQL database.

How did I discover this?

I set up an ILIAS 6 instance and started monitoring database queries, esp. what happened when I set up PDF Generation. Among other things I discovered the column names and table storing the setup information for the Java RPC server. I compared these to ILIAS 7 and found that the respective values were not set and were basically unsettable through the webGUI because that part of the interface was just missing. Oops.

How to fix this?

At first I looked at the PHP units for the interface but they are very convoluted. It was confusing and I didn't find the right code region. Changing the PHP code probably wouldn't survive an update anyhow, so I abandoned the idea. Instead I turned to the database directly and just set the values manually. I guess short of a schema change the settings will survive an update. But who knows. Here is how you do it:

$ mysql -u root -p

USE iliasdb;
SHOW COLUMNS FROM setttings;
SELECT value FROM settings WHERE keyword = 'rpc_server_host';   # Just check if the field is empty.
SELECT value FROM settings WHERE keyword = 'rpc_server_port';   # Just check if the field is empty.
UPDATE settings SET value = 'localhost' WHERE keyword = 'rpc_server_host';
UPDATE settings SET value = '11111' WHERE keyword = 'rpc_server_port';
COMMIT; 

That's it.

How do I feel?

I feel upset. I wasted so much time on this. In the end it is a stupid bug because I sincerely do not hope that it was a conscious design decision to remove a section you need to configure an important funnctionality of a LMS. If it was I bloody expect it to be mentioned in the documentation in plain text because not everybody spends his whole day in the ILIAS community and codebase. I mean, a whole section of the admin interface is missing!

Anger aside, I guess there are better ways to achieve the outcome I needed but the less than good documentation does not mention anything about it. I would be happy to hear about it. You can post any suggestions in my main thread at the ILIAS support forum [1]

[1] Hopefully this links to the thread at ILIAS support forum. Don't you just love ILIAS? If not, search for "Has anybody a screenshot"