" Is there some kind of seal around the plunger which may have
disintegrated?

There's a flap valve at the bottom of the siphon that has probably failed."

The flap valve is a disc of flexible plastic material like polythene
and it will wear at the edges, becomeing less effective and failing to
lift the water up the syphon, as you describe.

Drain the cistern, remove the syphon, take it apart, take the flap
valve disc to a plumbers' merchants and get a new one. If it's not bog
standard, or if it's a designer job with parts only available by
special order, it might be sensible to source the bits before you
dismantle it, to minimize the inconvenience.