Ifö Spira was leaking. After opening it up the leaking was found to be caused by the filling valve leaking past its seal, causing it to spray water outside of the inner container. The water spraying is only happening when the filler valve is just opening. When it is either fully open or fully closed, the seals are working as expected. See the water coming out to the left in this video when the valve is half open:

The upper part of the mechanism looks like this:

The filler mechanism can be removed and disassembled:

The plunger has its aged and therefore faulty rubber seal mounted in the middle of the plunger. The rubber part at the end is for sealing off the water from the main pipe. Now for the fix. An O-ring fits inside the seal:

By putting four O-rings on the plunger, the original seal gets just big enough to start working as a seal again:

The suitable O-ring was found to be “R-04” from my Clas Ohlson O-ring box:

Note: Ifö/Geberit seems to have updated this construction to RSK-Nr: 779 04 35

The Ifö/Geberit spare parts page says that the new version was introduced 2021.