> but does not exercise executive or policy-making power

This is largely but not entirely true. It's also largely true by convention/Realpolitik ("try and exercise your powers and see how long you stay king!") and not by law.

> absolute monarchies (in which a monarch is the only decision-maker)

The monarch was essentially never the only decision maker in absolute monarchies. Nominally, yes. In practice, not at all. Going against too many established interested was seriously bad for the monarch's health.