Thank you for the tips; the sound problem seems to have gotten better after my general cleaning. The mystery clip is not the smallest one I've seen on the machine, but I will keep looking for any obvious spots which could be missing one. Could also be that it's something that was lost and already replaced earlier during the machine's lifetime.
This gets a bit embarrassing, but just as I thought I'm done with maintenance on this particular machine, it seems like I have accidentally introduced a new problem:
After the general cleaning I put everything back together and went on to test the machine.
The problem is that now the line spacing system doesn't work properly! The part (pawl?) which is supposed to do it only works properly if I use the return lever very slowly.
This problem pretty much renders the machine unusable again. I must have bumped into something there when I was inserting the platen back for the second time, which I had to remove again for the general cleaning, and which is a bit more challenging when compared to the carriage-shifted Tippas, thanks to the large plastic card guide being on the way.
Both of my carriage-shifted Tippas have this mechanism in full working order, and it looks very similar as on the Tippa S, so I should have replacement parts if I actually broke something beyond repair. I filmed a short video in order to demonstrate the problem better: